Question

67. The sides of a rectangle are in the ratio
of 3 : 2 and its perimeter is 50 cm. The
area of the rectangle (in cm²) is
(1) 75
(2) 100
(3) 135 (4) 150​

Answer 1

Question:-

The sides of a rectangle are in the ratio of 3 : 2 and its perimeter is 50 cm. The area of the rectangle (in cm²) is

• (1) 75
• (2) 100
• (3) 135
• (4) 150

Required Answer:-

Given:-

$\\ \sf{\rightarrow{The\:ratio\:of\:the\:sides\:of\:a\:rectangle\:is\:3\ratio 2}}$

$\sf{\rightarrow{The\:perimeter\:of\:the\:rectangle\:is\:50cm}}$

To Find:-

$\\ \\ \sf{\rightarrow{The\:area\:of\:the\:rectangle}}$

Solution:-

Let,

• Length of the rectangle be 3x
• Breadth of the rectangle be 2x

As we know that:-

$\\ \underline{\boxed{\rm{\blue{\bold{Perimeter\:of\:a\:rectangle }= 2(l + b)}}}}$

Where,

• l stands for length
• b stands for breadth.

According to the question:-

$\\ \\ \sf{\bold{2(3x + 2y) = 50}}$

$\\ \sf{\implies{5x = \frac{50}{2} }}$

$\\ \sf{\implies{x = \frac{25}{5} }}$

$\\ \sf{\therefore{x = \pink{5}}}$

Therefore:-

$\\ \sf{Length\:of\:the\:rectangle\:is = 3 \times 5 = \bold{15}}$

$\sf{Breadth\:of\:the\:rectangle = 2 \times 5 = \bold{10}}$

Again,

$\\ \underline{\boxed{\rm{\blue{\bold{Area\:of\:a\:rectangle }= l \times b}}}}$

Substituting the values:-

$\\ \sf{\bold{Area\:of\:a\:rectangle }= 15cm \times 10cm}$

$\\ \sf{\bold{Area\:of\:a\:rectangle }= (15 \times 10)cm {}^{2} }$

$\\ \sf{\bold{Area\:of\:a\:rectangle }= \red{150 {cm}^{2} } }$

$\\ \\ \underline{\boxed{\rm{Hence,\:\bold{4)150}\:is\:the\:correct \: option}}}$

Answer 2

(4) 150

Area of the Rectangle is 150 cm²

Step-by-step explanation:

Solution :

Let,

Length of Rectangle (L) = 3x

Breadth of Rectangle (B) = 2x

Perimeter of Rectangle is 50 cm.

Perimeter of Rectangle = 2 (L + B)

⇒ 2 (3x + 2x) = 50

⇒ 5x = 50 / 2

⇒ 5x = 25

⇒ x = 25 / 5

⇒ x = 5

Length of Rectangle (L) = 3x

⇒ 3x

⇒ 3 (5)

⇒ 15

Length of Rectangle = 15 cm

Breadth of Rectangle (B) = 2x

⇒ 2x

⇒ 2 (5)

⇒ 10

Breadth of Rectangle = 10 cm

★ Area of the Rectangle :

Area of the Rectangle = (L× B)

⇒ 15 × 10

⇒ 150

Area of the Rectangle = 150 cm²

∴ Area of the Rectangle is 150 cm²