This picture of a wall hanging is made of congruent 30° − 60° − 90° triangles with height 6 cm and hypotenuse 12 cm. What is the perimeter of the wall hanging to the nearest tenth of a centimeter?

A. (24+243√) cm ≈ 65.6 cm
B. (12+6) cm = 18.0 cm
C. (144+36) cm = 180 cm
D. (12+123√) cm ≈ 32.8 cm

28.4cm

Step-by-step explanation:

Perimeter of the wall will be the sum if all the sides of the right angled triangle.

Given the height of the triangle = 6cm

Hypotenuse = 12cm

Using Pythagoras theorem to get the third side

Hypotenuse² = opposite²+adjacent²

Taking the height as the opposite = 6cm

12² = 6²+adj²

Adj² = 12²-6²

Adj² = 144-36

Adj² = 108

Adj = √108

Adj = 10.39cm

The perimeter of the wall = 6cm+12cm+10.39cm

= 28.39cm

= 28.4cm to nearest tenth.

5050

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