Question

the base of a triangle is 24 cm and the corresponding altitude is 16 cm the area of a rhombus is equal to the area of triangle if one of the diagonal of the Rhombus is 20cm find the length of the Other diagonal

Answer 1

Hello,

Area of a triangle = 1/2 *base *height
So, area of the given triangle is :-
$\frac{1}{2} \times 24 \times 16 \\ 1 \times 12 \times 16 = 196 {cm}^{2}$
Now,
Area of triangle =area of rhombus.

So, the area of rhombus = 196 cm²

One diagonal of rhombus (d1) = 20 cm

We know that the area of a rhombus is :-
$\frac{1}{2} \times d1 \times d2$
Where d1 and d2 are the two diagonals of the rhombus.
So
$\frac{1}{2} \times 20 \times d2 = 196 \\ 10 \times d2 = 196 \\ d2 = \frac{196}{10} = 19.6cm$
The length of the other diagonal is 19.6 cm

Hope this will be helping you ✌️