The lenght of a rectangle is 10cm greater than its width. The perimeter of the rectangle is 1m. A.Find the simplest expression for the perimeter for the rectangle if the width is x.B. Find the width of the rectangle. C. Calculate the area of the rectangle. Answers: A=20+x .B=20 .C=600
width = x
length = (x+10)
P = 2x + 2(x+10) = 4x+20
4x+20 = 100
x + 5 = 25
x = 20
A = x(x+10) = x^2 + 10 x
= 400 + 200
= 600
To solve this problem, we can follow these steps:
A. Find the simplest expression for the perimeter of the rectangle if the width is x:
The perimeter of a rectangle is equal to twice the sum of its length and width. Let's call the width of the rectangle "x". According to the problem, the length is 10 cm greater than the width, so it can be expressed as "x + 10 cm".
Therefore, the perimeter (P) can be calculated as follows:
P = 2(length + width) = 2(x + x + 10 cm) = 2(2x + 10 cm) = 4x + 20 cm.
So the simplest expression for the perimeter is P = 20 + 4x cm.
B. Find the width of the rectangle:
As given in the problem, the perimeter of the rectangle is 1m. Since 1m is equal to 100 cm, we can set up the equation:
20 + 4x = 100
Now, we solve for x:
4x = 100 - 20
4x = 80
x = 80/4
x = 20
Therefore, the width of the rectangle is 20 cm.
C. Calculate the area of the rectangle:
The area of a rectangle can be calculated by multiplying its length by its width. In this case, the length is x + 10 cm and the width is x. Substituting these values, we get:
Area = length * width = (x + 10 cm) * x = x^2 + 10x cm^2.
Plugging in the width we found in step B (x = 20 cm), we get:
Area = 20^2 + 10*20 cm^2 = 400 + 200 cm^2 = 600 cm^2.
Therefore, the area of the rectangle is 600 cm^2.