SOLUTION: A right triangle and a square share a side. The hypotenuse of the triangle measures 10 cm. One base of the triangle measures 4 cm. Neither the known base nor the hypotenuse is the

Algebra ->  Angles -> SOLUTION: A right triangle and a square share a side. The hypotenuse of the triangle measures 10 cm. One base of the triangle measures 4 cm. Neither the known base nor the hypotenuse is the       Log On


   

Question 767524: A right triangle and a square share a side. The hypotenuse of the triangle measures 10 cm. One base of the triangle measures 4 cm. Neither the known base nor the hypotenuse is the side that is shared with the square. Find the area of the square.
Found 2 solutions by reviewermath, CountrySLP:
Answer by reviewermath(1029) About Me  (Show Source):
You can put this solution on YOUR website!
Q:
A right triangle and a square share a side. The hypotenuse of the triangle measures 10 cm. One base of the triangle measures 4 cm. Neither the known base nor the hypotenuse is the side that is shared with the square. Find the area of the square.
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A:

Using Pythagorean Theorem:
s%5E2+%2B+4%5E2+=+10%5E2
s%5E2 = 10%5E2+-+4%5E2 = highlight%2884%29.
The area of the square is highlight%2884%29 cm%5E2

Answer by CountrySLP(2) About Me  (Show Source):
You can put this solution on YOUR website!
Actually the answer would be 84 (not 84%5E2) See below:
The length of the third triangle side would be solved as follows:
a%5E2+%2B+b%5E2+=+c%5E2, ie.
4%5E2+%2B+b%5E2+=+10%5E2
16+%2B+b%5E2+=+100
b%5E2+=+100+-+16
b+=+sqrt%2884%29 which will be slightly larger than 9
This makes sense, because 10, as the hypotenuse, would be the longest side.
Therefore, one side of the square would be sqrt%2884%29.
Now, the area of the square would be computed as follows:
a+=+s%5E2
a+=+%28sqrt%2884%29%29+%2A+%28sqrt%2884%29%29
a+=+84