SOLUTION: find the exact length of the side of a square which has a diagonal of 100 ft. The hypotenuse of a right triangle measures 100 inches, and one leg measures 50 inches. find t

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These use the Pythagorean theorem which states that if you have two legs of a right triangle, say a and b, and a hypotenuse, c, then:



In the first problem you need to remember that the sides of a square have the exact same length and that the interior angles of a square all measure 90 degrees. This means that the diagonal forms a right triangle with two of the sides. so to find the side lengths you can use the formula above where c = 100 feet.

a^2 + b^2 = c^2 where b and c are the same so this really becomes
2a^2 = c^2

now we just need to plug in numbers and solve.

2a^2 = 100
a^2 = 50
a =
a =

Now for the second problem. We know that one of the legs is 50 inches, lets call this a. our c value is 100 inches so now all we need to do is solve for b.

a^2 + b^2 = c^2
50^2 + b^2 = 100^2
2500 + b^2 = 10000
b^2 = 7500
b =
b =
b =

thats your answer for part a.

part b is = 86.602