Question

The length of a rectangle is greater than twice
its breadth by 10 cm. The length of its digonal
is 25 cm. Find the length and
breadth of the
rectangle. Fill in the bloxes to get the solution .​

Answer 1

Answer: 24

Step-by-step explanation:

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