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Alchen
2 months ago
15

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
Mathematics
1 answer:
Svet_ta [12.7K]2 months ago
6 0

Answer:

28.4 cm

Step-by-step explanation:

The perimeter of the triangular wall is determined by adding all sides of the right triangle.

The triangle's height is given as 6 cm.

The hypotenuse measures 12 cm.

Using the Pythagorean theorem to find the third side:

Hypotenuse² = opposite² + adjacent²

Assigning the height as opposite = 6 cm, we find:

12² = 6² + adj²

Thus, adj² = 12² - 6²

Which gives us adj² = 144 - 36

So, adj² = 108

Leading to adj = √108

Thus, adj = 10.39 cm

The perimeter totals = 6 cm + 12 cm + 10.39 cm

= 28.39 cm

= 28.4 cm when rounded to the nearest tenth.

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