Posted by **G** on Thursday, July 8, 2010 at 6:13pm.

The area of a rectangle is 24, and its diagonal is radical 52. Find its dimensions and perimeter.

Longer side = ?

Shorter side = ?

Perimeter = ?

- math -
**drwls**, Thursday, July 8, 2010 at 8:12pm
Let the dimensions be a and b.

ab = 24

a^2 + b^2 = 52

a^2 + (24/a)^2 = 52

a^4 -52a^2 + 576 = 0

(a^2 -36)(a^2 -16)

a^2 = 36 or 16

a = 6 or 4

b = 4 or 6

- math -
**Sara**, Thursday, July 8, 2010 at 9:11pm
Thank You!

- math -
**Henry**, Thursday, July 8, 2010 at 11:19pm
Let X and Y represent the sides of

the rectangle.

X^2 + Y^2 = 52 = diagonal squared.

XY = 24 =the area of rectangle.

y = 24/X

X^2 + (24/X)^2 = 52

X^2 +576/X^2 = 52

Multiply both sides by x^2 :

X^4 + 576 = 52X^2

X^4 - 52X^2 + 576 = 0. used computer to

help find roots: X = -4, X = 4, X = -6,

X = 6. Select the positive roots:

The sides are 4 and 6. P = (2*4) +(2*6)

= 20

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