A rectangle has a perimeter of 32 and an area of 56. Find the length of its diagonal.

Guest Jan 8, 2020

#1**+3 **

2 l + 2w = 32

l * w = 56 l = 56/w

Sub second into first equation

112/w + 2w = 32 multiply by w

2w^2 - 32w + 112 = 0 Quadratic formula shows w = 8+ 2 sqrt 2 then l = 8-2sqrt2

d^2 = (8+ 2 sqrt2)^2 + (8-2 sqrt2)^2

d^2 = 144 d = 12

ElectricPavlov Jan 8, 2020

#2**0 **

Another similar way as EP

Width = x, Height = y

2x+2y=32

xy=56

So x+y=16

Square it

x^2+y^2+2xy=256

Plug in xy=56

x^2+y^2=144

Diagonal is sqrt of that, so 12.

You are very welcome!

:P

CoolStuffYT Jan 8, 2020