Answer:
106.08 and 47.13 feet
Step-by-step explanation:
We have that the area of a rectangle is equal to the multiplication of one side by the other side, that is:
a = x * y
we know that the area is 5000, therefore:
5000 = x * y
y = 5000 / x
they tell us that the diagonal measures 10 feet more than one side, let's say on the x side, therefore the diagonal measures x + 10.
A right triangle is formed, which by the Pythagorean equation has the following form:
(x + 10) ^ 2 = x ^ 2 + y ^ 2
if we replace the value of and we are left with:
(x + 10) ^ 2 = x ^ 2 + (5000 / x) ^ 2
x ^ 2 + 20 * x + 100 = x ^ 2 + 5000 ^ 2 / x ^ 2
20 * x + 100 = 5000 ^ 2 / x ^ 2
20 * x ^ 3 + 100 * x ^ 2 = 25000000
from here we obtain that the value of x is equal to 106.08
now the value of y:
y = 5000 / 106.08
y = 47.13
therefore the measurements are 106.08 and 47.13 feet
