Answer:
Sides of the rectangle are 3 and 4
Explanation:
x=width
y=length
Area = xy = 12
x = 12/y plug this in to the next equation
x² + y² = 5² = 25
(12/y)² + y² = 25
144/y² + y² = 25 multiply by y² on both sides
144 + y⁴ = 25y² rewrite the equation
y⁴ -25y² + 144 = 0
rewrite with z=y² and z²=y⁴
z² - 25z + 144 = 0 now you can use the quadratic formula to find the roots of z (a=1, b=-25, c=144). Consider only the positive roots of z:
z = 16, 9
z = y² = 16, 9
y = √16, √9
y = 4, 3
x = 12/4 = 3
x = 12/3 = 4
x = 4 = length
y = 3 = width