A Rangoli has been drawn on a floor of a house. ABCD and PQRS both are in the shape of a rhombus. Find the radius of semicircle drawn on each side of rhombus ABCD.
Solution:
Given, ABCD and PQRS are rhombus.
We have to find the radius of the semicircle drawn on each side of rhombus ABCD.
Considering rhombus ABCD,
AO = PA + PO
= 2 + 2
AO = 4 units
Similarly, BO = BQ + QO
= 2 + 1
BO = 3 units
We know that the diagonals of a rhombus bisect each other at 90 degrees.
So, OAB is a right angled triangle.
Considering triangle OAB,
AB² = OA² + OB²
AB² = (4)² + (3)²
AB² = 16 + 9
AB² = 25
Taking square root,
AB = 5 units
From the figure, AB is the diameter of the semicircle.
We know, radius = diameter / 2
Radius = 5/2
= 2.5 units
Therefore, the required radius is 2.5 units.
✦ Try This: 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.
☛ Also Check: NCERT Solutions for Class 8 Maths
NCERT Exemplar Class 8 Maths Chapter 5 Problem 158
A Rangoli has been drawn on a floor of a house. ABCD and PQRS both are in the shape of a rhombus. Find the radius of semicircle drawn on each side of rhombus ABCD.
Summary:
A Rangoli has been drawn on a floor of a house. ABCD and PQRS both are in the shape of a rhombus. The radius of semicircle drawn on each side of rhombus ABCD is 2.5 units.
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