document.write( "Question 252306: An isosceles triangle has a 10-inch base and two 13-inch sides. What other value,
\n" ); document.write( "in inches, can the base have and still produce a triangle with the same area? \n" ); document.write( "

Algebra.Com's Answer #184157 by drk(1908) $\"\"$ $\"About$

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step 1: draw a triangle and label the parts: base = 10 and legs = 13.
\n" ); document.write( "step 2: draw an altitude from the top vertex to the base. It should be parallel to the base. What this does is cut the base in half - 5 and 5.
\n" ); document.write( "step 3: use pythagorean theorem to find the height.
\n" ); document.write( " $\"a%5E2+%2B+b%5E2+=+c%5E2\"$
\n" ); document.write( " $\"5%5E2+%2B+b%5E2+=+13%5E2\"$
\n" ); document.write( " $\"b%5E2+=+144\"$
\n" ); document.write( " $\"b+=+12\"$ .
\n" ); document.write( "The area of a triangle is A = (1/2)bh. FOR us, this is A = (1/2)(10)(12) = 60.
\n" ); document.write( "we want a list of all triangles whose bh = 120. These are answers as (base,height)
\n" ); document.write( "(1,120), (2,60), (3,40), (4,30), (5,24), (6,20), (8,15), and (10,12), but we can't use this as it was the question. So, we get 7 options assuming integers only. The question says nothing about integer sides. \n" ); document.write( "

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