Question 134230
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:<br>

{{{a^2 + b^2 = c^2}}}<br>

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.<br>

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

now we just need to plug in numbers and solve.<br>

2a^2 = 100
a^2 = 50
a = {{{sqrt(50)}}}
a = {{{5 sqrt(2)}}}<br>

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.<br>

a^2 + b^2 = c^2
50^2 + b^2 = 100^2
2500 + b^2 = 10000
b^2 = 7500
b = {{{sqrt(7500)}}}
b = {{{10sqrt(75)}}}
b = {{{50sqrt(3)}}}<br>

thats your answer for part a.<br>

part b is {{{50sqrt(3)}}} = 86.602