If the side of a rhombus is 10 cm and one diagonal is 16 cm, the area of the rhombus is 96 cm². Is the given statement true or false and justify your answer.
Solution:
Given, the side of the rhombus = 10 cm
Length of one diagonal = 16 cm
Area of rhombus = 96 cm²
We have to determine if the given statement is true or false.
Consider a rhombus PQRS
We know that all the sides of a rhombus are equal in length.
Diagonal PR = 16 cm
We know that the diagonals of a rhombus bisect each other at right angles.
PO = OR
PO = 1/2 PR
PO = 1/2 (16)
PO = 8 cm
In triangle POQ,
By using Pythagorean theorem,
PQ²= OP² + OQ²
(10)² = (8)² + OQ²
100 - 64 = OQ²
OQ² = 36
Taking square root,
OQ = 6 cm
Now, the diagonal SQ = 2(OQ)
= 2(6)
SQ = 12 cm
Area of rhombus = 1/2 × product of diagonals
= 1/2 × PR × SQ
= 1/2 × 16 × 12
= 8 × 12
Area = 96 cm²
Therefore, the given statement is true.
✦ Try This: Write True or False and justify your answer: If the side of a rhombus is 8 cm and one diagonal is 6 cm, the area of the rhombus is 46 cm²
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 12
NCERT Exemplar Class 9 Maths Exercise 12.2 Problem 5
If the side of a rhombus is 10 cm and one diagonal is 16 cm, the area of the rhombus is 96 cm². Is the given statement true or false and justify your answer.
Summary:
The given statement “If the side of a rhombus is 10 cm and one diagonal is 16 cm, the area of the rhombus is 96 cm²” is true
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