Problema Solution

The area of a rectangle is 32, and its perimeter is 24 . Find its dimensions and diagonal.

Longer side:

Shorter side:

Diagonal:

Answer provided by our tutors

Solution:

x = longer side

y = shorter side

z = diagonal

 

xy = 32

y = 32/x

 

2x + 2y = 24

2x + 2(32/x) = 24

2x^2 + 64 = 24x

x^2 - 12x + 32 = 0

(x-8)(x-4) = 0

x = 8

x = 4

 

Since x = longer, x = 8

y = 32/8

y = 4

 

z = sqrt(x^2+y^2)

z = sqrt(8^2 + 4^2)

z = 4 sqrt(5)

 

Longer side: 8

Shorter side: 4

Diagonal: 4 sqrt(5)