document.write( "Question 624705: A triangle has an 8-in base and a height of 4-in. A second triangle has three-fourths the area and half the height of the first triangle. What is the base of the second triangle? \n" ); document.write( "
Algebra.Com's Answer #393130 by math-vortex(648)\"\" \"About 
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document.write( "Hi, there-\r\n" );
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document.write( "The Problem:\r\n" );
document.write( "A triangle has an 8-in base and a height of 4-in. A second triangle has three-fourths the area and \r\n" );
document.write( "half the height of the first triangle. What is the base of the second triangle?\r\n" );
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document.write( "Solution:\r\n" );
document.write( "The formula for the area of a triangle is A=(1/2)*b*h where b is its base and h is its height.\r\n" );
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document.write( "We see that the first triangle has a base of 16 square inches (sq. in.) because,\r\n" );
document.write( "A=(1/2)(8)(4)=16\r\n" );
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document.write( "The second triangle has three-fourths the area of the first triangle. Its area is 12 sq. in. because\r\n" );
document.write( "(3/4)(16)=12\r\n" );
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document.write( "The height of the second triangle is 2-inches because it's half of 4-inches.\r\n" );
document.write( "(1/2)(4)=2\r\n" );
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document.write( "Now we know the area of the second triangle and its height. Substitute 12 for A and 2 for h into the\r\n" );
document.write( "area formula.\r\n" );
document.write( "A=(1/2)*b*h\r\n" );
document.write( "12=(1/2)*b*(2)\r\n" );
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document.write( "Solve for b.\r\n" );
document.write( "b=12\r\n" );
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document.write( "The base of the second triangle is 12 inches.\r\n" );
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document.write( "It's always a good idea to check your work against the conditions of original problem:\r\n" );
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document.write( "\"A second triangle has three-fourths the area ... of the first triangle.\"\r\n" );
document.write( "[12] is three-fourths of [16]. TRUE!\r\n" );
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document.write( "\"A second triangle has ... half the height of the first triangle.\"\r\n" );
document.write( "[2] is half of [4]. TRUE!\r\n" );
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document.write( "That's it. Please email me if you have questions or comments about the solution. I'm happy to \r\n" );
document.write( "explain further and I always appreciate feedback.\r\n" );
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document.write( "Ms.Figgy\r\n" );
document.write( "math.in.the.vortex@gmail.com \r\n" );
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