Question

the area of a parallelogram with base 24.8cm and altitude 16.5 cm is equal to the area of a rhombus whose diagonal is 22 cm. find the length of the other diagonal of the rhombus.

Answer 1

Other diagonal = Area of 1st ||gm=Area of 2nd ||gm
Base=24.8
Altitude=16.5
Area=Base×Altitude
=409
Then the other area
=22×x
409=22×x
X=409/22
=18.6
Other diagonal=18.6
=409=22×18.6
=409=409
Solution verified.

Answer 2

✬ Length of other diagonal = 37.2 cm ✬

Step-by-step explanation:

Given:

• Area of parallogram = Area of rhombus
• Measure of base of parallogram is 24.8 cm
• Measure of height of parallogram is 16.5 cm
• Measure of diagonal of rhombus is 22 cm.

To Find:

• What is the length of other diagonal of rhombus.

Formula to be used:

• Area of parallogram = Base x Height
• Area of rhombus = 1/2 x d¹ x d²

Solution: Let the other diagonal of rhombus be d². Since, both areas are equal to each other, Therefore,

$\implies{\rm }$ Base x Height = 1/2 x d¹ x d²

$\implies{\rm }$ (24.8 x 16.5) = (1/2 x 22 x d²)

$\implies{\rm }$ 409.2 = 11d²

$\implies{\rm }$ 409.2/11 = d²

$\implies{\rm }$ 37.2 cm = d²

Hence, the measure of other diagonal of rhombus is 37.2 cm

________________

★ ChEck ★

→ Base x Height = 1/2 x d¹ x d²

→ (24.8 x 16.5) cm² = (1/2 x 22 x 37.2) cm²

→ 409.2 cm² = 11 x 37.2 cm²

→ 409.2 cm² = 409.2 cm² { LHS = RHS }