Question

7. The area of a rhombus is equal to the area of a triangle. If the base of the triangle is 28 cm, its corresponding
altitude is 18 cm and one of the diagonals of a rhombus is 21 cm, find its other diagonal.​

Answer 1

Given :-

• base of triangle = 28 cm
• height of triangle = 18 cm
• area of rhombus = area of triangle
• one diagonal of rhombus = 21 cm

To Find :-

• find the other diagonal of rhombus?

Solution :-

we know that,

$\underline{ \boxed{ \bold{area \: of \triangle = \frac{1}{2} \times b \times h }}}$

$\bold{: \implies \frac{1}{ \cancel2} \times 28 \times \cancel{18} } \\ \\ \bold{: \implies28 \times 9} \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{: \implies 252 \: {cm}^{2} } \: \: \: \: \: \: \: \:$

so, the area of the triangle is 252 cm²

and we know that,

if ‘d1’ and ‘d2’ are two diagonals of the rhombus, then

$\underline{\boxed{ \bold{area \: of \: rhombus = \frac{1}{2} \times d1 \times d }}}$

• and it is given that area of rhombus = area of triangle

$\bold{: \implies \frac{1}{2} \times 21 \times d2 = 252 } \\ \\ \bold{: \implies d2 = \frac{ \cancel{252 }\times 2}{ \cancel{21}} } \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{: \implies d2 = 12 \times 2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{: \implies d2 = 24 \: cm} \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

hence, other diagonal of the rhombus is 24 cm

Answer 2

Given :

The area of a rhombus is equal to the area of a triangle. Base of the triangle is 28 cm, its corresponding  altitude is 18 cm and one of the diagonals of a rhombus is 21 cm.

To find :

Other diagonal of rhombus.

Solution :

Base of triangle = 28 cm

Corresponding altitude = 18 cm.

∴ Area of triangle = 1/2 × b × h

⇒ Area of triangle = 1/2 × 28 × 18

⇒ Area of triangle = 14 × 18

⇒ Area of triangle = 252 cm²

∵ Area of triangle = Area of rhombus.

∴ Area of rhombus = 252 cm²

Also, one diagonal of rhombus, d₁ = 21 cm

∵ Area of rhombus = 1/2 × d₁ × d₂

So atq,

⇒ 252 = 1/2 × 21 × d₂

⇒ 21d₂ = 252 × 2

⇒ 21d₂ = 504

⇒ d₂ = 504/21

⇒ d₂ = 24 cm.

∴ Other diagonal of rhombus = 24 cm.