Question

Find the perimeter of a rhombus whose diagonals are 16cm and 12cm​

Answer 1

Answer:

Given:

Diagonal,d1 = 16 cm

Diagonal,d2 = 12 cm

To find out:

Find the perimeter of a rhombus ?

Solution:

We know, Diagonal of rhombus bisect each other at right angles.

AC = 16 cm, OC = 1/2 AC ⇒ 1/2 × 16 = 8 cm

BD = 12 cm, OD = 1/2 BD ⇒ 1/2 × 12 = 6 cm

By using pythagoras therome

DC² = OC² + OD²

DC² = 8² + 6²

DC² = 64 + 36

DC² = 100

DC = 10 cm

Therefore,

DC = BC = AD = AB = 10 cm [ All sides are equal ]

Now,

perimeter of rhombus = 4 ( Side )

= 4 × 10

= 40 cm

Answer 2

$\huge \fcolorbox{red}{green}{ \red{40cm}}$

Step-by-step explanation:

Q.

Find the perimeter of a rhombus whose diagonals are 16 cm and 12 cm

.

Solution -

Given -

Diagonal 1 (p) = 16 cm

Diagonal 2 (q) = 12 cm

.

$perimeter = 2 \sqrt{ {p}^{2} + {q}^{2} } \\ \\ = 2 \sqrt{ {16}^{2} + {12}^{2} } cm \\ \\ = 2 \sqrt{256 + 144} cm \\ \\ = 2 \sqrt{400} cm \\ \\ = 2 \times 20cm \\ \\ = 40cm$

Hence perimeter = 40 cm.

hope it helps.