Question

Area of a square is 1 sq. meter more than ½ of the area of the rectangle. If area of   square is 91 sq. metre. Then find the dimentions of the rectangles . Given breadth is ¾ times of length
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Answer 1

Answer:-

Let the area of the rectangle be "x" m².

Given:

Area of a square = 91 m²

Area of the square is 1 m² more than half the area of the rectangle.

→ Area of the square = (1/2 * x + 1) m²

→ 91 m² = (x + 2) / 2

On cross multiplication we get,

→ 91 * 2 = x + 2

→ 182 = x + 2

→ 182 - 2 = x

→ x = 180 m²

→ Area of the rectangle = 180 m²

And also given that,

breadth is 3/4th of length.

→ breadth = 3*length/4 -- equation (1)

We know that,

Area of a rectangle = length * breadth.

Hence,

→ length * breadth = 180

Putting the value of breadth from equation (1) we get,

→ length* (3 * length ) / 4 = 180

→ (length)² * 3/4 = 180

→ (length)² = 180 * 4/3

→ (length)² = 240

→ (length)² = (15.4)²

→ length = 15.4 m (Approx.)

Substitute the value of length in equation (1)

→ Breadth = 3/4 * 15.4 m

→ Breadth = 11.55 m

Hence, the dimensions of the rectangle are 15.4 m and 11.55 m.