Question

12. The perimeter of a rectangle is 72 cm. The length is 3 times the width. Find the area of the rectangle
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Answer 1

Answer:

243 cm²

Explanation:

Let the width be 'w'

∴ Length = 3w

Perimeter of rectangle = 2(l + b)

72cm = 2(3w + w)

72 = 2(4w)

72 = 8w

9 = w

∴ Width of the rectangle = 9cm

and length = 27 cm [ Since l = 3(9) ]

Area of rectangle = l x b unit²

= 9 x 27

= 243 cm²

∴ Area of the rectangle is 243 cm²

Answer 2

• Area of rectangle is 243 $\sf cm^{2}$.

Explanation:

Given:-

• Perimeter of rectangle is 72 cm.

To find:-

• Area of rectangle.

Solution :-

Let, Width be 'x'.

And Length be '3x'.

We know that,

$\boxed{ \star \: \bold{ \sf Perimter \: of \: rectangle = 2(l + b)}}$

In which,

• l and b are Length and breadth or Width of rectangle respectively.

Perimeter = 72 cm.

Put perimeter in formula:

$\longrightarrow \sf 72 = 2 \times (3x + x)$

$\longrightarrow \sf 72 = 6x + 2x$

$\longrightarrow \sf 72 = 8x$

$\longrightarrow \sf \cfrac{72}{2} = x$

$\longrightarrow \sf 9 = x$

Or, x = 9

We have taken x be Width. So, Width of rectangle is 9 cm.

And We have taken length be 3x = 3 × 9 = 27 cm.

So, Length of rectangle is 27 cm.

We know :

$\boxed{ \star \: \bold{Area \: of \: rectangle = l \times b}}$

$\longrightarrow \sf 27 \times 9$

$\longrightarrow \sf 243$

Therefore,

Area of rectangle is 243 $\sf cm^{2}$.