Question

The length of a rectangle is 9cm more than its breadth. Its area is 36cm2.find the length and breadth

Answer 1

Answer:

Step-by-step explanation:

Let the breadth of the rectangle be x cm.

Therefore, length =x+9 cm

Area of rectangle=length ×breadth

36cm^2=(x+9)x

36=x^2+9x

x^2+9x-36=0

x^2+12x-3x-36=0

x(x+12)-3(x+12)=0

(x+12)(x-3)=0

Therefore, x+12=0 or x-3=0

x=-12 or 3

But measurements can't be negative,

So, x=3

Answer:

Breadth = x = 3cm

Length = x+9 = 3+9 = 12cm

Answer 2

ATQ, the length of a rectangle is 9cm more than it's breadth.

let the breadth of the rectangle be x cm

therefore it's length = x + 9 cm

given the area of the rectangle = 36cm²

formula to find the area of a rectangle is length × breadth

➡ length × breadth = 36cm²

➡ (x + 9)(x) = 36cm²

➡ x² + 9x = 36cm²

➡ x² + 9x - 36 = 0

using splitting the middle term method,

➡ x² + (12x - 3x) - 36 = 0

➡ x² + 12x - 3x - 36 = 0

➡ x(x + 12) - 3(x + 12) = 0

➡ (x + 12) (x - 3)

therefore x = -12 or x = 3

since length can't be in negative

so the breadth of the rectangle = x = 3cm

and the Length of the rectangle = x + 9 = 12cm

verification :-

= 3 × 12

= 36cm²