Question

The dimensions of four rectangles are given below. Which has an area different from the area of each of the other three?

Answer 1

To determine which of the rectangles has a different area, the areas of the four rectangles must be calculated. The rectangle with a different area is rectangle b

The dimension of the 4 rectangles are:

a. length: 4x and width: 4

b. length: 11 and width: x

c. length: 2 and width: 8x

d. length: 16x and width: 1

The area of a rectangle is:

$Area = Length \times Width$

Rectangle (a)

$Area = 4x \times 4$

$Area = 16x$

Rectangle (b)

$Area = 11 \times x$

$Area = 11x$

Rectangle (c)

$Area = 2 \times 8x$

$Area = 16x$

Rectangle (d)

$Area = 16x \times 1$

$Area = 16x$

Rectangles (a), (c) and (d) have the same area (i.e. 16x) while rectangle (b) has 11x as its area.

Hence, the rectangle with a different area is rectangle (b).

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