sir / madam , pls can you give the answers for the 2 questions below pls , 1 *the base - Maths - Mensuration

Question

sir / madam ,
pls can you give the answers for the 2 questions below pls ,
1 *the base of the parallelogram is twice the height if the area
is 578 square cm , find the base and the height ?
2 **in a parallelogram ABCD , AB = 18cm,BC =12 cm AE
perpendicular to DC , AF perpendicular to BC and if AE = 6 4cm ,
find the lenght of AF ?

Lalit Mehra · Accepted Answer

Dear Student!

(1)

Let the height of the parallelogram be x cm.

Given, base of the parallelogram = 2 × height of the parallelogram = 2x cm.

We know that,

Area of parallelogram = Base × Corresponding height

$\Rightarrow 578 = 2 x \times x \Rightarrow x^{2} = \frac{578}{2} {cm}^{2} = 289 {cm}^{2} \Rightarrow x = \sqrt{289} cm = 17 cm$

∴ Height of the parallelogram = 17 cm

Base of the parallelogram = 2 × 17 cm = 34 cm

(2)

We know that,

Area of parallelogram = Base × Corresponding height of the parallelogram

⇒ BC × AF = CD × AE

⇒ 12 cm × AF = 18 cm × 6.4 cm ( $∵$ CD = AB = 18 cm )

$\Rightarrow AF = \frac{6.4 \times 18}{12} cm = 9.6 cm ∴ AF = 9.6 cm$

Cheers!

We know that, Area of parallelogram = Base Ã— Corresponding height of the parallelogram â‡’ BC Ã— AF = CD Ã— AE â‡’ 12 cm Ã— AF = 18 cm Ã— 6 4 cm ( $∵$ CD = AB = 18 cm ) $\Rightarrow AF = \frac{6 4 \times 18}{12} cm = 9 6 cm ∴ AF = 9 6 cm$ Cheers!