Question

What is the combined perimeter of these two rectangles?

A)
6x + 14


B)
12x + 24


C)
12x + 26


D)
24x + 52

Answer 1

D

Explanation:

Perimeter is sum of all sides:

Purple rectangle:

Perimeter = 2[2x+7 + 4x+5]

= 2[6x + 12]

= 12x + 24

White rectangle:

Perimeter = 2[3x + 3x+14]

= 2[6x + 14]

= 12x + 28

Total Perimeter:

12x + 24 + 12x + 28

= 24x + 52

Answer 2

D) 24x + 52

Explanation:

The perimeter of the shaded rectangle

P = 2(l+w)

= 2(4x+5 + 2x+7)

Combine like terms

=2( 6x+12)

Distribute

= 12x+24

The perimeter of the unshaded rectangle

P =2(l+w)

= 2(3x+14 +3x)

Combine like terms

=2(6x+14)

Distribute

=12x+28

Add the perimeters together

12x+24+ 12x+28

Combine like terms

24x+52