Question

Each side a rhombus is 10 cm long and one of its diagonals measurs 16 cm. Find the length of the other diagonals and hence find the area of the rhombus.

Answer 1

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Answer 2

Answer:

$\huge\tt{Answer:}$

Given that :-

Each side a rhombus is 10 cm long and one of its diagonals measurs 16 cm.

To find:

the length of the other diagonals and hence find the area of the rhombus.

Diagonals of a rhombus bisect each other at right angles.

Let ABCD be the rhombus, Diagonal AC= 16 cm and side AB = 10 cm.

In right triangle AOB, AB = 10 cm, AO = 8 cm

By Pythagoras theorem, AB^2 = AO^2 + BO^2

(10)^2 = (8)^2 + BO^2

BO^2 = (10)^2 – (8)^2

BO = 6 cm

$\huge\boxed{Diagonal\: BD = 2 × 6 = 12 \:cm}$

Now,

$area \: of \: rhombus = \frac{1}{2} \times (product \: of \: rhombus)$

$\frac{1}{2} \times 16 \times 12 = 96 {cm}^{2}$

=> Hence length of other diagonal = 12 cm

=> Area of rhombus = 96 cm^2