Question

Q1.(a) Harish made a rectangular garden, with its length 5 metres more than its width. The next year,he increased the length by 3 metres and decreased tye width by 2 metres.If tye atea of the second garden was 119 sq m, was the second garden larger or smaller?
(b) The length of a rectangle exceeds its breadth by 5 m.If the breadth were doubled and the length reduced by 9 m,the area of the rectangle would have increased by 140 sq m.Find its dimensions.

Answer 1

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Answer 2

Answer and explanation:

(a) Given : Harish made a rectangular garden, with its length 5 meters more than its width. The next year,he increased the length by 3 meters and decreased the width by 2 meters. If the area of the second garden was 119 sq m.

To find : Was the second garden larger or smaller?

Solution :

Let breadth b=x

length be l=x+5

Then it became l=x+8 and b=x-2

Area of the rectangle be $A=lb$

$119=(x+8)(x-2)$

$119=x^2+8x-16-2x$

$x^2+6x-135=0$

$x^2+15x-9x-135=0$

$x(x+15)-9(x+15)=0$

$(x-9)(x+15)=0$

$x=9,-15$

Reject x=-15 so x=9.

Length = 9+5=14

Area of the rectangle be $A=9\times 14=126\ m^2$

Second garden is smaller.

(b) The length of a rectangle exceeds its breadth by 5 m.If the breadth were doubled and the length reduced by 9 m,the area of the rectangle would have increased by 140 sq m. Find its dimensions.

The length l=2x

Breadth b=x+5-9=x-4

Area of the rectangle be $A=2x(x-4)\ m^2$

According to question,

$2x(x-4)=140+x(x+5)$

$2x^2-8x=140+x^2+5x$

$x^2-13x-140=0$

$x^2-20x+7x-140=0$

$x(x-20)7(x-20)=0$

$x=20$

Breadth b=20 m and Length l=25 m.