Question

91. The area of a rectangle is 54 cm². If the length is 3 cm more than breadth, calculate the breadth.
(a) 9 cm
(b) 6 cm
(c) 12 cm
(d) 8 cm
10​

Answer 1

Answer:

(b) 6cm

Step-by-step explanation:

Area of rectangle= 54 cm square

Let breadth= x cm

Length= x+ 3 cm

So, x × ( x + 3 )= 54 cm square

or 6 × ( 6+3) = 54

The breadth is 6 cm.

Answer 2

Given

• Area of rectangle = 54 cm²
• Length of the rectangle is 3 cm more than the breadth

To find

• Breadth of the rectangle

Concept

We are having the value of the area of the rectangle that is 54 cm² and we are given that the length is 3 cm more than the breadth. So, firstly we will let the breadth be x and let the length be 3 cm more than it. That is, x + 3 cm. As we know, Area of rectangle is the product of its length and breadth. So, by substituting the values in it. We will find the value of x. By substituting the value of x in breadth, we will find its value.

Solution

Let the breadth and length of the rectangle be x cm and x + 3 cm respectively.

Using formula,

Area of rectangle = l × b

where,

• l = length of the rectangle
• b = breadth of the rectangle

Substituting the values,

⟶ (x + 3) * x = 54

⟶ x² + 3x = 54

⟶ x² + 3x - 54 = 0

⟶ x² + 9x - 6x - 54 = 0

⟶ x(x + 9) - 6(x + 9) = 0

⟶ (x - 6)(x + 9) = 0

• (x - 6) = 0

⟶ x - 6 = 0

⟶ x = 6

• (x + 9) = 0

⟶ x + 9 = 0

⟶ x = - 9 Reject - ve

Hence, the value of x = 6

∴ Dimensions of the rectangle :-

length of the rectangle = x + 3 = 6 + 3 = 9 cm

Breadth of the rectangle = x = 6 cm

________________________________

Let's verify :-

Area of the rectangle = l × b

⟶ 9 × 6

⟶ 54 cm²

∴ Area of the rectangle = 54 cm²

Hence, verified.