Un predio rectangular tiene un área de 5000 pies^2. Una diagonal entre las esquinas opuestas mide 10 pies mas que un lado del predio, cuáles son las dimensiones del predio?

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