document.write( "Question 645496: 1. The height of a triangle is 2 m more than twice the length of the base. The area of the triangle is 42 m2. Find the height of the triangle.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "2.a2 – 3a = 28 \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "3.(a − 4)(a + 6) = −16
\n" ); document.write( " \r
\n" ); document.write( "\n" ); document.write( "4. 5y(y + 6) = 4(y + 6)
\n" ); document.write( "

Algebra.Com's Answer #405509 by MathLover1(20849)\"\" \"About 
You can put this solution on YOUR website!
1. The height of a triangle \"h\" is \"2m\" more than twice the length of the base \"a\".\r
\n" ); document.write( "\n" ); document.write( "=>... \"h=2a%2B2m\"...=>..\"h-2m=2a\" =>..\"a=%28h-2m%29%2F2\"\r
\n" ); document.write( "\n" ); document.write( "The area of the triangle \"A\" is \"A=42m%5E2\". \r
\n" ); document.write( "\n" ); document.write( "Find the height of the triangle.\r
\n" ); document.write( "\n" ); document.write( "\"A=%281%2F2%29a%2Ah\"\r
\n" ); document.write( "\n" ); document.write( "\"42m%5E2=%281%2F2%29a%2Ah\"........replace \"a\" with \"%28h-2m%29%2F2\"\r
\n" ); document.write( "\n" ); document.write( "\"42m%5E2=%281%2F2%29%28h-2m%29%2F2%2Ah\"...solve for \"h\"\r
\n" ); document.write( "\n" ); document.write( "\"42m%5E2=%28%28h-2m%29%2F4%29%2Ah\"\r
\n" ); document.write( "\n" ); document.write( "\"42m%5E2=%28%28h-2m%29h%2F4%29\"\r
\n" ); document.write( "\n" ); document.write( "\"42m%5E2=%28%28h%5E2-2hm%29%2F4%29\"\r
\n" ); document.write( "\n" ); document.write( "\"42m%5E2%2A4=h%5E2-2hm\"\r
\n" ); document.write( "\n" ); document.write( "\"168m%5E2=h%5E2-2hm\"\r
\n" ); document.write( "\n" ); document.write( "\"0=h%5E2-2hm-168m%5E2\"...or\r
\n" ); document.write( "\n" ); document.write( "\"h%5E2-2hm-168m%5E2=0\"....use quadratic formula to find \"h\"\r
\n" ); document.write( "\n" ); document.write( "\"h+=+%28-%28-2%29+%2B-+sqrt%28+%28-2%29%5E2-4%2A1%2A%28-168%29+%29%29%2F%282%2A1%29+\"\r
\n" ); document.write( "\n" ); document.write( "\"h+=+%282+%2B-+sqrt%284%2B672+%29%29%2F2+\"\r
\n" ); document.write( "\n" ); document.write( "\"h+=+%282+%2B-+sqrt%28676+%29%29%2F2+\"\r
\n" ); document.write( "\n" ); document.write( "\"h+=+%282+%2B-+26%29%2F2+\"\r
\n" ); document.write( "\n" ); document.write( "solution: we need only positive solution since the height cannot be negative\r
\n" ); document.write( "\n" ); document.write( "\"h+=+%282+%2B+26%29%2F2+\"\r
\n" ); document.write( "\n" ); document.write( "\"h+=+28%2F2+\"\r
\n" ); document.write( "\n" ); document.write( "\"highlight%28h+=+14m+%29\"\r
\n" ); document.write( "\n" ); document.write( "now find the length of the base \"a\"\r
\n" ); document.write( "\n" ); document.write( "\"a=%28h-2m%29%2F2\"\r
\n" ); document.write( "\n" ); document.write( "\"a=%2814m-2m%29%2F2\"\r
\n" ); document.write( "\n" ); document.write( "\"a=%2812m%29%2F2\"\r
\n" ); document.write( "\n" ); document.write( "\"highlight%28a=6m%29\"\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "2.\r
\n" ); document.write( "\n" ); document.write( "\"a%5E2-3a+=+28\" \r
\n" ); document.write( "\n" ); document.write( "\"a%5E2-3a+-28=0\" \r
\n" ); document.write( "\n" ); document.write( "\"a+=+%28-%28-3%29+%2B-+sqrt%28+%28-3%29%5E2-4%2A1%2A%28-28%29+%29%29%2F%282%2A1%29+\"\r
\n" ); document.write( "\n" ); document.write( "\"a+=+%283+%2B-+sqrt%289%2B112%29%29%2F2+\"\r
\n" ); document.write( "\n" ); document.write( "\"a+=+%283+%2B-+sqrt%28121%29%29%2F2+\"\r
\n" ); document.write( "\n" ); document.write( "\"a+=+%283+%2B-+11%29%2F2+\"\r
\n" ); document.write( "\n" ); document.write( "solutions:\r
\n" ); document.write( "\n" ); document.write( "\"a+=+%283+%2B11%29%2F2+\"\r
\n" ); document.write( "\n" ); document.write( "\"a+=+17%2F2+\"\r
\n" ); document.write( "\n" ); document.write( "\"highlight%28a+=+7%29+\"\r
\n" ); document.write( "\n" ); document.write( "or\r
\n" ); document.write( "\n" ); document.write( "\"a+=+%283+-11%29%2F2+\"\r
\n" ); document.write( "\n" ); document.write( "\"a+=+-8%2F2+\"\r
\n" ); document.write( "\n" ); document.write( "\"highlight%28a+=+-4+%29\"\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "3.\r
\n" ); document.write( "\n" ); document.write( "\"%28a+-4%29%28a+%2B+6%29+=-16\"
\n" ); document.write( "
\n" ); document.write( "\"a%5E2%2B6a+-4a+-24+=-16\"\r
\n" ); document.write( "\n" ); document.write( "\"a%5E2%2B2a-24+%2B16=0\"\r
\n" ); document.write( "\n" ); document.write( "\"a%5E2%2B2a-8=0\"\r
\n" ); document.write( "\n" ); document.write( "\"a+=+%28-2+%2B-+sqrt%28+2%5E2-4%2A1%2A%28-8%29+%29%29%2F%282%2A1%29+\"\r
\n" ); document.write( "\n" ); document.write( "\"a+=+%28-2+%2B-+sqrt%28+4%2B32+%29%29%2F2+\"\r
\n" ); document.write( "\n" ); document.write( "\"a+=+%28-2+%2B-+sqrt%28+36+%29%29%2F2+\"\r
\n" ); document.write( "\n" ); document.write( "\"a+=+%28-2+%2B-+6%29%2F2+\"\r
\n" ); document.write( "\n" ); document.write( "solutions:\r
\n" ); document.write( "\n" ); document.write( "\"a+=+%28-2+%2B+6%29%2F2+\"\r
\n" ); document.write( "\n" ); document.write( "\"a+=+4%2F2+\"\r
\n" ); document.write( "\n" ); document.write( "\"highlight%28a+=2%29+\"\r
\n" ); document.write( "\n" ); document.write( "or\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"a+=+%28-2-+6%29%2F2+\"\r
\n" ); document.write( "\n" ); document.write( "\"a+=+-8%2F2+\"\r
\n" ); document.write( "\n" ); document.write( "\"highlight%28a+=-4%29\"
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "4. \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "\"5y%28y+%2B+6%29+=+4%28y+%2B+6%29\"...first multiply\r
\n" ); document.write( "\n" ); document.write( " \"5y%5E2+%2B+30+=+4y+%2B+24\"\r
\n" ); document.write( "\n" ); document.write( "\"5y%5E2+%2B+30+-4y+-24=0\"\r
\n" ); document.write( "\n" ); document.write( "\"5y%5E2+-4y%2B+6+=0\"\r
\n" ); document.write( "\n" ); document.write( " \"y+=+%28-%28-4%29+%2B-+sqrt%28+%28-4%29%5E2-4%2A5%2A6+%29%29%2F%282%2A5%29+\"\r
\n" ); document.write( "\n" ); document.write( "\"y+=+%284+%2B-+sqrt%2816-120+%29%29%2F10+\"\r
\n" ); document.write( "\n" ); document.write( "\"y+=+%284+%2B-+sqrt%28-104+%29%29%2F10+\"\r
\n" ); document.write( "\n" ); document.write( "\"y+=+%284+%2B-+sqrt%28%28-1%29104+%29%29%2F10+\"\r
\n" ); document.write( "\n" ); document.write( "\"y+=+%284+%2B-+i%2Asqrt%28104+%29%29%2F10+\"\r
\n" ); document.write( "\n" ); document.write( "\"y+=+%284+%2B-+10.2i%29%2F10+\"\r
\n" ); document.write( "\n" ); document.write( "solutions:\r
\n" ); document.write( "\n" ); document.write( "\"y+=+%284+%2B+10.2i%29%2F10+\"\r
\n" ); document.write( "\n" ); document.write( "\"y+=+4%2F10+%2B+10.2i%2F10+\"\r
\n" ); document.write( "\n" ); document.write( "\"highlight%28y+=+0.4%2B+1.02i%29+\"\r
\n" ); document.write( "\n" ); document.write( "or\r
\n" ); document.write( "\n" ); document.write( "\"y+=+%284+-+10.2i%29%2F10+\"\r
\n" ); document.write( "\n" ); document.write( "\"y+=+4%2F10+-+10.2i%2F10+\"\r
\n" ); document.write( "\n" ); document.write( "\"highlight%28y+=+0.4-+1.02i+%29\"\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\n" ); document.write( "
\n" );