Q. The perimeter of a rectangle is 34 cm and the length is longer than the breadth by 7 cm. The areaof the rectangle is :

Q. The perimeter of a rectangle is 34 cm and the length is longer than the breadth by 7 cm. The area of the rectangle is :

(A) 40 cm².

(B) 60 cm².

(C) 238 cm².

(D) 64 cm².

Answer:- (B) 60 cm².

Let the breadth of the rectangle be x cm. Then the length will be x+7 cm.

• The perimeter of a rectangle is given by: 2×(length+breadth)=34
• Substituting the values: 2×(x+x+7)=34Simplifying this:

  $$\Rightarrow \; 2\times (2x+7)=34$$

  ⇒ 4x + 14 = 34⇒ 4x+14=34
  $$\Rightarrow \; 4x=34-\; 14\; =20$$⇒ x= 20/4

  $$\Rightarrow$$x= 5

• So, the breadth x is 5 cm, and the length ($x+7)$ is (5 +7) =12 cm.
• The area of the rectangle is: length×breadth=12cm ×5cm=60 cm².

Thus, the area of the rectangle is 60 cm².