KnowledgeBoat Logo
|

Mathematics

The diagonal of a rectangle is 60 m more than its shorter side and the larger side is 30 m more than the shorter side. Find the sides of the rectangle.

Quadratic Equations

14 Likes

Answer

Let diagonal be x m,

Shorter side = (x - 60) m

Larger side = (x - 60 + 30) = (x - 30) m

In rectangle,

(Diagonal)2 = (Length)2 + (Base)2

⇒ x2 = (x - 30)2 + (x - 60)2

⇒ x2 = x2 + 900 - 60x + x2 + 3600 - 120x

⇒ x2 = 2x2 - 180x + 4500

⇒ 2x2 - x2 - 180x + 4500 = 0

⇒ x2 - 180x + 4500 = 0

⇒ x2 - 150x - 30x + 4500 = 0

⇒ x(x - 150) - 30(x - 150) = 0

⇒ (x - 30)(x - 150) = 0

⇒ x - 30 = 0 or x - 150 = 0

⇒ x = 30 or x = 150.

Since, shorter side is 60 less than hypotenuse and side cannot be negative

∴ x ≠ 30.

Shorter side = (x - 60) m = (150 - 60) = 90 m

Larger side = (x - 30) m = (150 - 30) = 120 m

Hence, sides of rectangle are 90 m and 120 m.

Answered By

7 Likes

Related Questions