193k views
3 votes
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:

User Fidd
by
7.2k points

1 Answer

4 votes

Answer:

(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

Given the following rectangles, identify all combinations of assembling these rectangles-example-1
User Csilk
by
7.0k points