Question

In rhombus DLMP, DM= 24 cm, m∠LDO = 43° and DL = 13 cm. Find each of the following.(i)OM(ii)m∠DOL(iii)m∠DLO(iv)PL

Answer 1

Step-by-step explanation:

In the rhombus ABCD, AC and BD are the diagonals. If the diagonals are 24 cm and 10 cm. Find the length of each of its sides.

A 13 cm

B 12 cm

C 5 cm

D 10 cm

ANSWER

We know that, diagonals in a rhombus bisect each other perpendicularly.

Let O is the intersecting point of diagonals AC and BD.

OA=2AC=224=12cm

OB=2BD=210=5cm

Now, in △AOB,∠AOB=90o

⇒  (AB)2=(OA)2+(OB)2                [ By Pythagoras theorem ]

⇒  (AB)2=(12)2+(5)2

⇒  (AB)2=144+25

⇒  (AB)2=169

∴  AB=13cm

We know that, all sides of rhombus are equal.

∴   The length of each side of rhombus is 13cm