Question

Given: △DMN, DM=10√3 m∠M=75°, m∠N=45° Find: Perimeter of △DMN

Answer 1

Correct Answer is: Perimeter of ΔDMN is 54.873 units.

Solution:-

Given that DM=10√3,m∠M=75°,m∠N=45°

So,m∠D= 180-(75+45) = 60°

So to find perimeter we need other 2 sides also.

Let us use sine rule to find them.

$\frac{DM}{sin(N)}=\frac{DN}{sin(M)} =\frac{MN}{sin(D)}$

$\frac{10\sqrt{3} }{sin(45)} = \frac{DN}{sin(75)}=\frac{MN}{sin(60)}$

$DN=\frac{10\sqrt{3} }{sin(45)}Xsin(75) = 23.66$

$MN=\frac{10\sqrt{3} }{sin(45)} Xsin(60)=21.213$

Hence perimeter = DM+MN+DN

                             = 10+21.213+23.66

                             =54.873 units