# math

posted by G

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

Longer side = ?
Shorter side = ?
Perimeter = ?

1. drwls

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

2. Sara

Thank You!

3. Henry

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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