The diagonals of a rhombus are 8 cm and 15 cm. Find its side.
Solution:
Given, the diagonals of a rhombus are 8 cm and 15 cm.
We have to find the side of the rhombus.
In a rhombus, opposite sides are parallel and the opposite angles are equal.
All the sides of a rhombus are equal in length, and the diagonals bisect each other at right angles.
Consider a rhombus ABCD,
Let AB = 15 cm and BD = 8 cm
OA = OC = 15/2 = 7.5 cm
OB = OD = 8/2 = 4 cm
Since the diagonals bisect each other at 90 degrees, it divides the rhombus into two congruent triangles.
Considering triangle AOB,
AOB is a triangle right angled at O,
By pythagorean theorem,
AB² = OA² + OB²
AB² = (7.5)² + (4)²
AB² = 56.25 + 16
AB² = 72.25
Taking square root,
AB = 8.5 cm
We know that the sides of a rhombus are equal in length.
Therefore, the length of each side is 8.5 cm.
✦ Try This: This: The diagonals of a rhombus are 10 cm and 20 cm. Find its side
☛ Also Check: NCERT Solutions for Class 8 Maths
NCERT Exemplar Class 8 Maths Chapter 5 Problem 132
The diagonals of a rhombus are 8 cm and 15 cm. Find its side.
Summary:
The diagonals of a rhombus are 8 cm and 15 cm. The length of each side is 8.5 cm.
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