Question

The base and height of a rhombus are 10cm and 18cm respectively. One of the diagonals is 9, find the other

Answer 1

40cm

Answer:

Area of Rhombus = base × height ...[1]

and also

$\rm Area \ of \ Rhombus = \dfrac{1}{2} \times d_1 \times d_2 \qquad ...[2]$

Therefore,

$\rm base × height =\dfrac{1}{2}\times d_1 \times d_2$

In the above formula, d₁ and d₂ are the diagonals of the rhombus.

We have the length of one diagonal, base and height, so we can find the other diagonal length

Hence,

$\rm \dashrightarrow 10cm \times 18cm =\dfrac{1}{2}\times 9cm \times d_2$

$\rm \dashrightarrow d_2= \dfrac{2 \times 10cm \times 18cm}{9cm}$

$\rm\dashrightarrow d_2= 2 \times 10cm \times 2$

$\rm\dashrightarrow d_2= 40cm$

Hence, the length of another diagonal is 40cm.