Question

can you solve this question

Answer 1

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

Solution :
Let ABCD be rhombus.

We know that rhombus is type of parallelogram whose all sides are equal.
∴ AB = BC = CD = DA = 10 cm
Let the diagonals AC and BD intersect each other at O, where AC = 16 cm and let BD = x
We know that the diagonals of a rhombus are perpendicular bisectors of each other.
∴​ ∆AOB is a right angle triangle, in which OB = BD ÷ 2 = x ÷ 2 and OA = AC ÷2 = 16 ÷ 2 = 8 cm.
Now, AB= OA2 + OB2…by pythagoras theorem
∴ 102 = ( )2 + 82
ie. 100 − 64 =
36 ×4 = x2
∴ x2 =144
∴ x = 12 cm
Hence, the length of the other diagonal is 12 cm
We know that area of rhombus is,
Area of rhombus = × ( Diagonal1) × ( Diagonal2)
Hence,
Area of ABCD = × AC × BD
= × 16 × 12
= 96 cm2
Hence, the area of rhombus is 96 cm2