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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Question 134230: 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 the measure of the other leg.
a) give its length in simplified radical form.
b) Round the answer to the nearest thousandth.
I dont like word problems could you help me?
Thank U :)

Answer by algebrapro18(249) About Me  (Show Source):
You can put this solution on YOUR website!
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:

a%5E2+%2B+b%5E2+=+c%5E2

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 = sqrt%2850%29
a = 5+sqrt%282%29

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 = sqrt%287500%29
b = 10sqrt%2875%29
b = 50sqrt%283%29

thats your answer for part a.

part b is 50sqrt%283%29 = 86.602