Question

The length of a rectangle exceeds its width by 7 m. If the width is
decreased by 3 m and the length is decreased by 10 m, the area is
decreased by 95 sq.m. Find the dimensions of the rectangle.

Answer 1

$\sf{\huge{\underline{\green{Given :-}}}}$

• The length of a rectangle exceeds its width by 7 m. If the width is decreased by 3 m and the length is decreased by 10 m .

$\sf{\huge{\underline{\green{To\:Find :-}}}}$

• The dimensions of the rectangle.

$\sf{\huge{\underline{\green{Answer :-}}}}$

Let the width of rectangle be x,

According to the question,

• The length of a rectangle exceeds its width by 7 m.

So, it's length = ( x + 7 )

The width is decreased by 3 m and the length is decreased by 10 m.

• length = ( x + 7 ) - 10 = x - 3

• width = x - 3

The area of rectangle = x × (x + 7)

• New width = (x - 3)m

• New length = (x + 7) - 10 = (x - 3)m

The new area =

➝ length × breadth

➝ (x-3)(x-3)

➝ (x-3)²

Area - New Area = 95 sq.m

➝ x(x+7) - (x-3)² = 95

➝ x² + 7x - x² - 9 + 6x = 95

➝ 13x = 95 + 9

➝ 13x = 104

➝ x = 104 / 13

➝ x = 8

The Dimensions of rectangle :-

• Width = 8m

• length = x + 7 = 8 + 7 = 15m

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