Question

6. The area of a rhombus is equal to the area of a triangle having base 24.8 cm and the
corresponding height 16.5 cm. If one of the diagonals of the rhombus is 22 cm, find the
length of the other diagonal.
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Answer 1

Answer:

Please find the attachment

Answer 2

To Find:-

• The lenght of the other diagonal.

Given:-

• Area of a triangle having base = 24.8 cm.
• The corresponding height = 16.5 cm.

Solution:-

Area of triangle = Area of rhombus

$\implies \dfrac{1}{2} \times Base \times Height = \dfrac{Product \: \: of \: Diagonals}{2}$

According to question,

$\dfrac{1}{2} \times 24.8 \times 16.5 = 22 \times \dfrac{x}{2}$

By simplifying,

$\implies204.6 = 22 \times \dfrac{x}{2}$

$\implies22x = 204.6 \times 2$

$\implies \: x = \dfrac{204.6 \times 2}{22}$

( By transposing 22 to R.H.S )

$\implies \: x = 9.3 \times 2$

$\implies \: x = 18.6$

Hence, The Length of other diagonal is 18.6 cm

$\bold{Required \: Answer}$

↪ Key Concepts ↩

• A parallelogram having all sides equal is called Rhombus.

• In a rhombus, all sides are parallel and equal.

• The diagonals bisect each other at right angle in a Rhombus.

• Area of Rhombus = 1/2 × d1 × d2