Question

A square and a rhombus have equal areas.
A diagonal of the square is 15v2 cm long,
If one of the diagonals of the rhombus is
22.5 cm long, find the length of its other
diagonal.​

Answer 1

Answer:

Length of other diagonal of rhombus is 20 cm.

$\rule{100}2$

Step-by-step explanation:

Given:

• A square and a rhombus have equal areas.
• Diagonal of square is 15√2 cm long.
• And one of the diagonals of the rhombus is 22.5 cm long.

Find:-

Length of other diagonals of rhombus.

Solution:-

Area of both rhmobus and square are equal.

Area of rhmobus = Area of square

1/2 (d1 × d2) = (side)²

Area of rhombus = 1/2 (d1 × d2)

Here -

d1 = length of diagonal 1 = 22.5 cm

d2 = length of diagonal 2 = ?

Substitute the known values in above formula.

⇒ 1/2 (22.5 × d2)

⇒ 11.25 × d2 ---- [1]

Now,

Diagonal of square = side√2

⇒ 15√2 = side√2

⇒ 15 = side

⇒ side = 15 cm

Area of square = (side)²

⇒ (15)²

⇒ 225 cm²

As, area of both rhombus and square are equal.

So,

⇒ 11.25 × d2 = 225

⇒ d2 = 225/11.25

⇒ d2 = 20 cm

Answer 2

$\boxed{\boxed{\mathtt{Answer\:=20cm}}}$

Given : Area of Square and Area of Rhombus is equal.

$\implies$ Diagonal of square =15√2

$\implies$ Diagonal of the rhombus = 22.5 cm.

To Find = The Lenght of Rhombus .

Step-By-Step-Explantation :

$\implies \:Diagonal\:of\:the\:square =\sqrt{2}\:side\\\\ \implies15\sqrt{2} = \sqrt{2}\:side\\\\\implies \:side\:=15cm\\\\ \implies\:area \: of \: the \: square = (15)^{2} = 225\:cm^{2}\\\\ \implies\:area\:of \: the \: square = area \: of \: rhombus\\\\ \implies\:225 \: cm^{2} = area \: of \: rhombus\\\\ \implies\:area \: of \: rhombus = \frac{1}{2} \times\:d_ 1\times\:d_2\\\\ \implies 225= \frac{1}{2}\times225\times \implies\:d _2\\\\ \implies\:d_2 =\frac{225 \times 2}{22.5}=\sf\cancel\dfrac{450}{22.5} =20\\\\\implies\:\therefore\: the\:length\:of\:other\:diagonal\: is\:20\:cm$