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:

$\frac{10}{5} = \frac{30}{x}$

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.