document.write( "Question 442336: the height of a triangle is 4 inches greater then twice its base.The area of the triangle is 168 square inches. What is the base of the triangle? \n" ); document.write( "

Algebra.Com's Answer #305086 by swincher4391(1107) $\"\"$ $\"About$

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Recall that A = 1/2bh.\r
\n" ); document.write( "\n" ); document.write( "We are given that h = 4+2b\r
\n" ); document.write( "\n" ); document.write( "So, putting it all together:\r
\n" ); document.write( "\n" ); document.write( "168 = 1/2 b(4+2b)\r
\n" ); document.write( "\n" ); document.write( "168 = 1/2(4b + 2b^2)\r
\n" ); document.write( "\n" ); document.write( "168 = 2b + b^2\r
\n" ); document.write( "\n" ); document.write( "b^2 + 2b - 168 = 0.\r
\n" ); document.write( "\n" ); document.write( "Something that multiplies to -168 and adds to 2? There's a trick to this. \r
\n" ); document.write( "\n" ); document.write( "Notice 13^2 = 169. So, it's more than likely in the middle of the two numbers we're trying to find. So let's try 12 and 14. Yep. 12 x 14 = 168. So this factors into (b+14)(b-12) So b = -14 or b =12. Is it possible to have a negative length on a base? No. So 12 must be our answer.\r
\n" ); document.write( "\n" ); document.write( "Let's check this. If 12 is our base, then according to our problem, 2*12 + 4 would be our height... or 28. so what is 12 * 28 /2?\r
\n" ); document.write( "\n" ); document.write( "196. Check.\r
\n" ); document.write( "\n" ); document.write( "Hope this helped! \n" ); document.write( "

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