Question

8. The perimeter of a rhombus is 40 cm and its diagonal is 12 cm. Find the length of other diagonal
Also, find the area of the rhombus.​

Answer 1

Given that the perimeter of a rhombus is 40 cm and its diagonal is 12 cm. We have to find out the other diagonal of the Rhombus.

Let's solve it :

We know,

Rhombus has 4 sides

It's perimeter will be 4a

Where,

a = Side of Rhombus

Now ,

• 4 a = 40
• a = 40/4
• a = 10 cm

Side of the Rhombus is 10 cm

Then ,

We know diagonal of rhombus bisect at 90°

Let we consider the mid point of the diagonals be ' O ' i.e, it divides the diagonal into two equal parts.

12/ 2 = 6 cm

Then , In ∆ DOC By using Pythagoras Theorem

• DO = 6 cm
• DC = 10 cm
• OC = ?

(Hypotenuse)² = (Perpendicular)² + (Base)²

→ (10)² = (6)² + (Base)²

→100 = 36 + (Base)²

→ 100 - 36 = (Base)²

→ 64 = (Base)²

→ √64 → Base

Base → 8 cm

Now, The other diagonal is AC which is nothing but

AO + OC = AC

8 + 8 = 16 cm

$\therefore\underline{\boxed{\textsf{Other Diagonal is = {\textbf{16 cm}}}}} \qquad\qquad \bigg\lgroup\bold{Required \ answer} \bigg\rgroup$

Answer 2

Answer:

Perimeter of rhombus= 40 cm

Side of rhombus = 10 cm

Length of other diagonal = 16 cm

$area = \frac{1}{2} \times product \: of \: diagonal \\ \\ = \frac{1}{2} \times 12 \times 16 \\ \\ = 84 \: \: {cm}^{2}$