# math

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

Longer side = ?
Shorter side = ?
Perimeter = ?

1. 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

posted by drwls
2. Thank You!

posted by Sara
3. 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

posted by Henry

## Similar Questions

1. ### Math

Find the Maximum area for the given perimeter of a rectangle. State the length and width of the rectangle. 28 inches Well, finally a calculus problem. Ok, we know that the area for a rectangle is A=l*w and the perimeter is
2. ### math

A square has the same area as a rectangle whose longer side is 2 times the length of its shorter side. If the perimeter of the rectangle is 24, what is the perimeter of the square? I have no idea how to do it. I need help.
3. ### Math

A square has the same area as a rectangle whose longer side is 2 times the length of its shorter side. If the perimeter of the rectangle is 24, what is the perimeter of the square? A. 8 sqrt 2 B. 16 sq

The shorter side of a rectangle is 20 m. Decreasing the longer side by 30 cm reduces the perimeter by one half. How long are the longer sides of the original rectangle? Explain the reasoning.
5. ### Geometry

A diagonal of a square has the same length as a diagonal of a rectangle. The area of the rectangle is 60% of the area of the square. What is the ratio of the shorter side to the longer side of the rectangle? Write your answer as a
6. ### Math

Checking my son's homework and want to see if he figured this out correctly .. i am too old to be revisiting this math ... Here is the question ... The perimeter of a rectangle patio is six times the length of the shorter side. If
7. ### Pre-Cal

The diagonal and the longer side of a rectangle make an angle of 43.2. If the longer side is 12.6cm, find the length of the shorter side.
8. ### algabra 2

One side of a triangle is 4 cm longer than the shortest side and 2 cm shorter than the longest side. The perimeter is 38 cm. Find the dimensions of the triangle.