SOLUTION: An isosceles triangle has a 10-inch base and two 13-inch sides. What other value, in inches, can the base have and still produce a triangle with the same area?

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Question 252306: An isosceles triangle has a 10-inch base and two 13-inch sides. What other value,
in inches, can the base have and still produce a triangle with the same area?
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
step 1: draw a triangle and label the parts: base = 10 and legs = 13.
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.
step 3: use pythagorean theorem to find the height.
a%5E2+%2B+b%5E2+=+c%5E2
5%5E2+%2B+b%5E2+=+13%5E2
b%5E2+=+144
b+=+12.
The area of a triangle is A = (1/2)bh. FOR us, this is A = (1/2)(10)(12) = 60.
we want a list of all triangles whose bh = 120. These are answers as (base,height)
(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.