Question

4 squares of the same size are placed side by side to make a single rectangle. the area of this new rectangle is 36 in². find its perimeter. a) 48 in. b) 12 in. c) 24 in. d) 30 in. e) 9 in. f) none of the above.

Explanation:

Step1: Find side - length of a square

Let the side - length of each square be $s$. The area of the new rectangle formed by 4 equal - sized squares is 36 in². Since the rectangle is made up of 4 squares, the area of one square is $A_{square}=\frac{36}{4}=9$ in². Using the formula for the area of a square $A = s^{2}$, if $A = 9$ in², then $s=\sqrt{9}=3$ in.

Step2: Determine the dimensions of the rectangle

When 4 squares are placed side - by - side, the length of the rectangle $l = 4s$ and the width $w=s$. Since $s = 3$ in, $l=4\times3 = 12$ in and $w = 3$ in.

Step3: Calculate the perimeter of the rectangle

The formula for the perimeter of a rectangle is $P=2(l + w)$. Substitute $l = 12$ in and $w = 3$ in into the formula: $P=2(12 + 3)=2\times15 = 30$ in.

Answer:

d) 30 in