Question

The perimeter of a rhombus is 60cm and one diagonal measure 18cm. find the length of the other diagonal learn

Answer 1

answer is 24cm.........

Answer 2

Answer:

24 cm

Step-by-step explanation:

Refer the attached figure

AC and BD are diagonals of rhombus

AC and BD bisects each other at right angles.

So , AO = OC = AC/2

BO = DO = BD/2

One diagonal measure = AC = 18cm

AO = AC/2 = 18/2 = 9 cm

Perimeter of rhombus = $4 \times side$

We are given that The perimeter of a rhombus is 60cm

So,  $4 \times side=60$

$Side=15$

So, AB =BC = CD = AD = 15 cm

In ΔAOB

$Hypotenuse^2=Perpendicular^2+Base^2$

$AB^2=AO^2+BO^2$

$15^2=9^2+BO^2$

$\sqrt{15^2-9^2}=BO$

$12=BO$

So, BD = 2BO = 2*12 = 24cm

Hence the length of the other diagonal is 24 cm