Question

Pqrs is a rhombus. The shorter diagonal pr measures 15 units and the measure of angle pqr is 60 degree . Find the length of a side of the rhombus.

Answer 1

Answer:

since it is rumbus its all sides are equal 

so pq=qr 

so the triangle pqr is an isosceles triangle

so angle qpr= (180-60)/2=60

since all angle of the triangle are equal . it is an equilateral triangle. so the side of rhombus is 12 units.

Answer 2

Concept

Rhombus is a special type of parallelogram having all of its four sides equal.

Given

1) PQRS is a rhombus

2) Shorter diagonal PR = 15 units

3) Angle PQR = 60

Find

Length of side of the rhombus

Solution

As we know that sides of rhombus are equal

PQ = QR

As two sides of triangle PQR are equal so its an isosceles triangle

So,

Angle PRQ = Angle RPQ

Angle PQR = 60     (Given)

Let Angle PRQ be x

In triangle PQR sum of all angles is 180

x + x + 60 = 180

2x + 60 = 180

2x = 120

x = 60

Hence the triangle is an equilateral triangle which means the length of all the sides is same

PQ = QR = PR = 15

The length of side of rhombus is 15 units.

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