Question

The area of a rhombus is equal to the area of a triangle having base 24.8cm and the corresponding height 16.5cm. If one of the diagonals of the rhombus is 22cm, find the length of the other diagonal.​

Answer 1

Answer:

Given:

Area of the rhombus = Area of the triangle

with base 24.8 cm and altitude 16.5 cm

1

Area of the triangle X base X

2

:: Area of the rhombus = 204.6 cm2

Also, length of one of the diagonals of the

rhombus=22 cm

1

We know: Area of rhombus (d1 x d2)

2

1

204.6 (22 x d2)

2

22 x d2 409.2

409.2

d2

= 18.6cm

22

Hence, the length of the other diagonal of

the rhombus is 18.6 cm.

Answer 2

$d_{2}$Answer:

Explanation:

Area of the triangle = $\frac{1}{2}$×base×height

                                  = $\frac{1}{2}$×24.8×16.5

                                  = 204.6 $cm^{2}$

Area of the rhombus = $\frac{1}{2}$×$d_{1}$×$d_{2}$

204.6 = $\frac{1}{2}$×22×$d_{2}$

$\frac{204.6 * 2}{22}$ = $d_{2}$

$d_{2}$ = 18.6 cm