Each side of a rhombus is 10cm long and one of its diagonals measures 16cm. Find the length of the other diagonal and hence find the area of the rhombus.

Question

Filo · Accepted Answer

We know that the diagonals of a rhombus bisect at right angles

We get

A O = OC = \frac{1}{2} A C

We know that

A C = 16 c m

A O = OC = \frac{1}{2} (16) = 8 c m

Consider

△ A OB

Using Pythagoras theorem

A B^{2} = A O^{2} + OB^{2}

by substituting values

10^{2} = 8^{2} + OB^{2}

OB^{2} = 100 - 64

OB^{2} = 36

OB = 6 c m

We know that the length of other diagonal

B D = 2 \times OB

By substituting the value

B D = 2 \times 6 = 12 c m

From the figure the area of

△ A BC = \frac{1}{2} \times A C \times OB

by substituting the values

△ A BC = \frac{1}{2} \times 16 \times 6

△ A BC = 48 c m^{2}

So we can calculate the area of rhombus as

Area of rhombus = area of

△ A BC +

area of

△ A C D

we get

Area of rhombus

= 48 + 8 = 96 c m^{2}

Therefore the length of other diagonal is

12 c m

and the area of rhombus is

96 c m^{2}

Question Text	Each side of a rhombus is $10 c m$ long and one of its diagonals measures $16 c m$ . Find the length of the other diagonal and hence find the area of the rhombus.
Answer Type	Text solution:1
Upvotes	150

Each side of a rhombus is $10 c m$ long and one of its diagonals measures $16 c m$ . Find the length of the other diagonal and hence find the area of the rhombus.

Text solutionVerified

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