$△ P Q R$ is a right-angled triangle at Q. If P = 30° and PQ = 8 cm, find the perimeter of the triangle.

8 (\sqrt{3} + 1)

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8 (\sqrt{3} + 2)

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8 (\sqrt{2} + 1)

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8 (\sqrt{3} + 3)

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Solution

The correct option is A $8 (\sqrt{3} + 1)$ cm
In $△ P Q R$
$c o s 30^{\circ} = \frac{P Q}{P R}$
$\frac{\sqrt{3}}{2} = \frac{8 c m}{P R}$
$P R = \frac{16}{\sqrt{3}} c m$
$t a n 30^{\circ} = \frac{Q R}{P Q}$
$\frac{1}{\sqrt{3}} = \frac{Q R}{8 c m}$
$Q R = \frac{8}{\sqrt{3}} c m$
Perimeter of triangle = PQ + QR + PR
Perimeter of triangle $= 8 c m + \frac{8}{\sqrt{3} c m} + \frac{16}{\sqrt{3} c m}$
Perimeter of triangle $= 8 c m + 8 \sqrt{3} c m$
Perimeter of triangle $= 8 (\sqrt{3} + 1) c m$

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△PQR is a right-angled triangle at Q. If P = 30° and PQ = 8 cm, find the perimeter of the triangle.

The correct option is A 8(√3+1) cmIn △PQR cos30∘=PQPR √32=8cmPR PR=16√3 cm tan30∘=QRPQ 1√3=QR8cm QR=8√3 cm Perimeter of triangle = PQ + QR + PR Perimeter of triangle =8cm+8√3cm+16√3cm Perimeter of triangle=8 cm+8√3 cm Perimeter of triangle =8(√3+1) cm

$△ P Q R$ is a right-angled triangle at Q. If P = 30° and PQ = 8 cm, find the perimeter of the triangle.