Question

the perimeter of a rhombus is 20 cm and one of its diagonal is 6 cm long find the length of other diagonal

Answer 1

HERE IS THE SOLUTION;

£ Given : Perimeter =20Cm.

length of one diagonal is 6 Cm.

Let AC be the first diagonal.

£ To find : Length of other diagonal.

£ Solution :

◆ We know that rhombus has 4 sides so, to get one side.

=> 24 = 4× Side.

=> Side = 24÷4 = 6Cm.

◆ We also know that diagonals of rhombus bisects each other at right angles and are equal.

So, In triangle AOD;

By Pythagoras Theorem;

AO= 1/2 AC

AO =1/2 × 6

AO=3Cm.

Also we know that side is 6Cm;

AD^2= DO ^2 + AO^2.

=> (6)^2= DO^2+ (3)^2

=> 36 = DO ^2 + 9

=> DO^2= 25

=>DO=5Cm.

◆ Since we know that BD is another diagonal &. DO = 1/2 BD.

=> BD = 2×DO

=> BD = 2×5

=> BD = 10 Cm.

◆◆ So the other diagonal is 10 Cm◆◆

HOPE IT HELPS

Answer 2

Above see.............