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What is the value of x in the triangle below?

What is the value of x in the triangle below?-example-1
User Ramy
by
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1 Answer

2 votes

Answer:

15 cm

Explanation:

All of the triangles in this figure are similar 30°-60°-90° triangles.

The ratio of shortest to longest sides in a 30°-60°-90° triangle is 1 : 2. This means the longest side of the largest triangle has length ...

2 × (10 cm) = 20 cm

It also means the shortest side of the smallest triangle is (10 cm)/2 = 5 cm.

The length shown as 'x' is the difference of these measures:

x = 20 cm -5 cm

x = 15 cm

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Additional comment

There are several "geometric mean" relations that apply to this sort of right-triangle geometry. One of them is that the side marked as 10 cm is the geometric mean of the short segment and the whole segment of the bottom edge. This will confirm that x = 15 cm.

(10 cm)² = (5 cm)(5 +15) cm = 100 cm²

User Haseena Parkar
by
5.0k points