Question

Given the following rectangles, identify all combinations of assembling these rectangles for which it is possible to create a rectangle with the length of and the width with no gaps or overlapping. You can't cut any of the rectangles but you may use some of them multiple times. More than one answer may be correct; mark all that apply. Rectangles you are given:

Answer 1

(b) and (d)

Explanation:

Given

See attachment for complete question

Required

Which group forms a rectangle of

`Length = 15`

`Width = 11`

First, calculate the area of the big rectangle

`Area = Length * Width`

`A_(Big) = 15 * 11`

`A_(Big) = 165`

Next, calculate the area of each rectangle A to E.

`A_A = 11 * 7`

`A_A = 77`

`A_B = 2 * 11`

`A_B = 22`

`A_C = 6 * 6`

`A_C = 36`

`A_D = 6 * 5`

`A_D = 30`

`A_E = 13 * 4`

`A_E = 52`

Then consider each option.

(a) 3E + 2B

`3E + 2B = 3 * 52 + 2 * 22`

`3E + 2B = 156 + 44`

`3E + 2B = 200`

(b) A + B + C + D

`A + B + C + D = 77+22+36+30`

`A + B + C + D = 165`

(c) 2C + 2D + 2B

`2C + 2D + 2B = 2 * 36 + 2 * 30 + 2 * 22`

`2C + 2D + 2B = 72 + 60 + 44`

`2C + 2D + 2B = 176`

(d) A + 4B

`A + 4B = 77 + 4 * 22`

`A + 4B = 77 + 88`

`A + 4B = 165`

(e) E + C + D + 3B

`E + C + D + 3B = 52 + 36 + 30 + 3 * 22`

`E + C + D + 3B = 52 + 36 + 30 + 66`

`E + C + D + 3B = 184`

Recall that:

`A_(Big) = 165`

Only options (b) and (d) match this value.

`A + B + C + D = 165`

`A + 4B = 165`

Hence, options (b) and (d) are correct