Question

the area of a rhombus is 28cm square and one diagonal is 4cm . find it's perimeter​

Answer 1

I hope the below answer helps you

Answer 2

GIVEN :

Area of a rhombus = 28cm

One diagonal = 4cm

Another diagonal = ?

We know that,

Area of rhombus = d1d2/2

According to the problem,

4 × d2 / 2 = 28

4 × d2 = 28 × 2

4 × d2 = 56

d2 = 56/4

d2 = 14cm

Thus, another diagonal = 14cm.

When two diagonal are bisected then there forms 4 triangles.

The two sides of triangle will be half of the two diagonals.

From rhombus ABCD,

We should take ∆ AEB

AO = 14/2 = 7cm

BO = 4/2 = 2cm

The third side = ?

From Pythagoras theorm,

(AB)² = (AO)² + (BO)²

(AB)² = 7² + 2²

(AB)² = 49 + 4

(AB)² = 53

AB = √53

Third side = √53

One side of rhombus = a = √53

Perimeter of rhombus :

= 4 × a

= 4√53cm

Therefore, perimeter of rhombus is 4√53cm.