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# 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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