The ratio of the width of rectangle P to the width of rectangle Q is 25 : 18.
In Mathematics and Geometry, the area of a rectangle can be calculated by using the following mathematical equation:
A = LW
Where:
- A represent the area of a rectangle.
- W represent the width of a rectangle.
- L represent the length of a rectangle.
Based on the information provided below, we translate the word problem into an algebraic expression and equation as follows;
"The length of Q is 25% more than the length of P" = 125% of 40;
Length of rectangle Q = 125/100 × 40
Length of rectangle Q = 50 cm
The area of rectangle P = length × width
The area of rectangle P = 40x square cm.
The area of rectangle Q = length × width
The area of rectangle Q = 50y square cm.
Since the area of rectangle Q is 10% less than the area of rectangle P, we have the following;
90% of 40x = 50y
90/100 × 40x = 50y
36x = 50y
x/y = 50/36
x/y = 25/18
x : y = 25 : 18
Complete Question:
P is a rectangle with length 40 cm and width x cm. Q is a rectangle with width y cm. The length of Q is 25% more than the length of P. The area of Q is 10% less than the area of P. Work out the ratio x : y. Give your answer in its simplest form.