Question

the length of a rectangle is greater than twice it's breath by 10 cm. the length of its diagonal is 25cm.find the length and breath of the 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