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Five identical rectangles are placed inside a square with side $24 cm$ as shown in the diagram. What is the area of one rectangle ?

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12 {cm}^{2}

16 {cm}^{2}

24 {cm}^{2}

32 {cm}^{2}

answer is D.

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Detailed Solution

Given, five identical rectangles are placed inside a square with side

24 cm

as shown in the diagram.
Question Image

Consider vertical line, let

b

h

be breadth and height of rectangle then,

24 = b + h + h + b

(vertically) .

b + h = 12 . . . . (1)

Consider the horizontal line. There are 2 heights involved and 1 breadth along with h - b.

24 = h + (h - b) + b + h

(horizontally)

3 h = 24

h = 8

Substituting

h = 8

in equation

(1)

b = 4

Area of a rectangle is length

\times

breadth.

\Rightarrow

Area

= bh = 8 (4)

\Rightarrow

Area

= 32 c m^{2}

So, the area is

32 c m^{2}

.
Hence, option 4 is correct.

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