Question

The length of a rectangle is greater than twice its breadth by 10cm. The length of its diagonal is 25cm. Find the length and breadth of rectangle.

Answer 1

ATQ, the length of the rectangle is greater than twice it's breadth by 10cm.

let the breadth of the rectangle be x.

therefore it's length = 2x + 10

given the length of the diagonal of rectangle = 25cm

➡ diagonal² = length² + breadth²

➡ 25² = (2x + 10)² + (x)²

➡ 625 = (2x)² + 2(2x)(10) + (10)² + x²

➡ 625 = 4x² + 40x + 100 + x²

➡ 625 - 100 = 5x² + 40x

➡ 5x² + 40x - 525 = 0

➡ x² + 8x - 105 = 0 (divided all by 5)

➡ x² + (15x - 7x) - 105 = 0

➡ x² + 15x - 7x - 105 = 0

➡ x(x + 15) - 7(x + 15) = 0

➡ (x + 15) (x - 7) = 0

therefore x = -15 or x = 7

since it can't be negative. x = 7cm

therefore the base of the rectangle = x = 7cm

and length of the rectangle = 2x + 10 = ( 2 × 7 )+ 10

= 14 + 10

= 24cm