Question

the length of rectangular garden is 15 meter longer than its breadth.find the length of the garden if its area is 2200 square meter. ?​

Answer 1

ATQ,

the Length of a rectangular garden is 15m longer than it's breadth.

let the breadth of the rectangular garden be x.

therefore it's length = x + 1

given the area of the rectangular garden = 2200m²

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

➡ length × breadth = 2200m²

➡ (x + 15)x = 2200m²

➡ x² + 15x = 2200m²

➡ x² + 15x - 2200 = 0

using splitting the middle term method, we get

➡ x² + (55x - 40x) - 2200 = 0

➡ x² + 55x - 40x - 2200 = 0

➡ x(x + 55) - 40(x + 55) = 0

➡ (x + 55) (x - 40)

➡ x = -55 or x = 40

since measurements can't be negative. so we'll take x as 40m.

hence,

• breadth of the rectangular garden = x = 40m

• length of the rectangular garden = x + 15 = 55m

VERIFICATION :-

= 40 × 55

= 2200m²

Answer 2

$\huge\bf{Answer}$

• 15m is the Length of a rectangular garden.

• The garden is longer than it's breadth.

• let y the breadth of the rectangular garden

• Hence ,we get the length = y + 1

• 2200m² is the Given the area of the Rectangular garden.

Using formula:-

(L×B) (Length × Breadth)

length × breadth = 2200m²

(y + 15)y = 2200m²

(y² + 15)y = 2200m²

(y² + 15)y - 2200 = 0

Using Middle Term method:-

y² + (55y - 40y) - 2200 = 0

y² + 55y - 40y - 2200 = 0

y(x + 55) - 40(y + 55) = 0

(y + 55) (y - 40)

y = -55 / y = 40

y = 40m

Therefore, y + 15 = 55m is the length of the rectangular Garden.

Checking the answer [Verification ]:-

= (40 × 55)

= [2200m]²