Math Prob 13?

Question

Find the dimensions of a rectangle that has area of 10 and a diagonal of length 5.

Answer 1

Let

L = length of rectangle
W = width of rectangle
A = area of rectangle
D = length of diagonal of rectangle

Given

A = LW = 10
D = 5

Find L and W.

A = LW = 10
W = 10/L

D² = L² + W²

25 = L² + W²
25 = L² + (10/L)²
25L² = L^4 + 100
L^4 - 25L² + 100 = 0
(L² - 20)(L² - 5) = 0
L = ±√20, ±√5
L = +2√5, +√5 (negatives are eliminated as length is positive)
L = +2√5 as L > W
W = +√5

The dimensions of the rectangle are L x W = 2√5 x √5.

Answer 2

It's all about the pythagorean theorem.
Now, you do the rest.