Question

the base of a parallelogram is 3cm more than its height and it's area is 40sq.cm. Find the base and height
(quadratic equation)​

Answer 1

Given :

• Base of parallelogram is 3cm more than its height.
• Area of parallelogram = 40 cm²

To find :

• Base and height of the parallelogram

Solution :

Let the

• Height of the parallelogram = x cm and
• Base of the parallelogram = x + 3 cm

Using formula,

Area of parallelogram = B × H

where,

• B = base of the parallelogram
• H = height of the parallelogram

Substituting the given values,

⇒ 40 = x × (x + 3)

⇒ 40 = x² + 3x

⇒ 0 = x² + 3x - 40

⇒ Product = - 40 x²

⇒ 0 = x² + 8x - 5x - 40

⇒ 0 = x(x + 8) - 5(x + 8)

⇒ 0 = (x - 5)(x + 8)

Taking (x - 5)

⇒ 0 = x - 5

⇒ - x = - 5

⇒ x = 5

Taking (x + 8)

⇒ 0 = x + 8

⇒ - x = 8

⇒ x = - 8 Reject - ve

∴ The value of x = 5

Substitute the value of x in Base and height.

Height of the parallelogram = x = 5 cm

Base of the parallelogram = x + 3 = 5 + 3 = 8 cm

________________________________

Let's verify :-

Substitute the value of x in 40 = x × (x + 3)

Taking Rhs,

⇒ x × (x + 3)

⇒ 5 × (5 + 3)

⇒ 5 × 8

⇒ 40

40 = 40

∴ Lhs = Rhs

Hence, verified.