Question

The area of a rhombus is equal to the area of a triangle whose base and the corresponding altitude are 24.8cm and 16.5cm respectively. If one of the diagonals of the rhombus is 22 find the length of the other diagonals.

Answer 1

Answer:

the other diagonal be q=24.8cm

Step-by-step explanation:

Given: the corresponding altitude are 24.8cm and 16.5cm and p=22cm

the area of the rhombus=pq/2

A=24.8×22/2

A=272.8

Answer 2

Given :

• Area of triangle = Area of rhombus
• Base of triangle = 24.8 cm
• Corresponding altitude of given base = 16.5 cm
• One of diagonal of rhombus = 22cm

To find :

Length of other diagonal

Formula used :

• Area of triangle = (1/2) base × altitude
• Area of rhombus = (1/2) Diagonal₁ × Diagonal₂

Solution :

Area of triangle = Area of rhombus

(1/2) Base × Height = (1/2) Diagonal₁ × Diagonal₂

$\sf \implies \: \dfrac{1}{2} \times 24.8cm \times 16.5cm \: = \: \dfrac{1}{2} \times 22cm \: \times d_{2} \\ \\ \sf \implies \: d_{2} \: = \: \dfrac{ \dfrac{1}{2} \times 24.8 \times 16.5 {cm}^{2} }{ \dfrac{1}{2} \times 22cm } \\ \\ \sf \implies \: d_{2} \: = \: \dfrac{12.4 \times 16.5cm}{11} \\ \\ \sf \implies \: d_{2} \: = \:12.4 \times 1.5cm \\ \\ \sf \implies \: d_{2} \: = \:18.6cm$

ANSWER :

Length of other diagonal = 18.6 cm