Question

A rectangle A with length 10 centimeters and width 5 centimeters is similar to another rectangle B whose length is 30 centimeters. Find the area of rectangle B.

Answer 1

Similarity means that the two rectangles have the same shape and proportions, but not the same size.

Set up a proportion for the two rectangles to find the missing width of rectangle B:


`(10)/(5) = (30)/(x)`

The numerator represents the length, and the denominator represents the width of the rectangles.

Cross multiply the fractions:


`10x = 150`

Divide both sides by 10 to get x by itself.


`x = 15`

The width of the second rectangle is 15 centimeters.

The area of a rectangle is given by the following:

width * length

Multiply the width by the length to find the area of this rectangle.


`30 * 15 = 450`

The area of rectangle B is 450 square centimeters.