If the size of a rectangle's area is twice as large as the size of it's perimeter, and the length of one of its sides is 4.5, what is the length of the other side?
one side --- 4.5
other side ---- x
area = 4.5x
perimeter = 2x + 9
translate " size of a rectangle's area is twice as large as the size of it's perimeter " into
4.5x = 2(2x+9)
4.5x = 4x + 18
.5x = 18
x = 36
the other side is 36
check:
area = 4.5(36) = 162
perimeter = 2(4.5+36) = 81
is 162 twice 81 ??? Sure is !
To solve this problem, we can set up an equation using the given information.
Let's say the length of the rectangle is L and the width is W.
We are given that the length of one of its sides is 4.5, so we can set up the equation:
L = 4.5
The area of a rectangle is given by the formula A = L * W, where A is the area, L is the length, and W is the width.
The perimeter of a rectangle is given by the formula P = 2 * (L + W), where P is the perimeter, L is the length, and W is the width.
We are given that the size of the rectangle's area is twice as large as the size of its perimeter, so we can set up the equation:
A = 2P
Substituting the formulas for area and perimeter, we get:
L * W = 2 * (L + W)
Now, let's substitute L = 4.5 into the equation:
4.5 * W = 2 * (4.5 + W)
Simplifying the equation, we get:
4.5W = 9 + 2W
Subtracting 2W from both sides:
2.5W = 9
Dividing both sides by 2.5:
W = 9 / 2.5
W ≈ 3.6
So, the length of the other side is approximately 3.6.