Question

3. The perimeter of a rhombus is 40 cm. If one
diagnonal is 16 cm, find :
() its another diagonal (ii) area
​

Answer 1

Answer:

12cm

Step-by-step explanation:

(I)we know that the diagonal of a rhombus bisects each other.

Answer 2

Answer:

12 cm, 96 cm²

Step-by-step explanation:

Given, perimeter of rhombus = 40 cm.

(i)

Let ABCD be the rhombus and diagonals BD, AC intersect at O.

∴ Side of rhombus = (1/4) * Perimeter

                               = (1/4) * 40

                              = 10 cm.

Let BD = 16 cm.

BO = (1/2) * BD

     = 8 cm.

Now,

AO = √AB² - BO²

     = √10² - 8²

     = √36

     = 6.

∴ AC = 2 AO = 2 * 6 = 12 cm.

(ii)

Area of rhombus = (1/2) * d₁ * d₂

                             = (1/2) * 16 * 12

                             = 96 cm².

Therefore:

(i) Another diagonal = 12 cm

(ii) Area of rhombus = 96 cm²

Hope it helps!