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The two triangles shown are similar - Junior Cycle Mathematics - Question 1 - 2013

Question 1

The two triangles shown are similar. Find the value of x. The left triangle has sides of length x and 6, and the right triangle has sides of length 25 and 15.

Worked Solution & Example Answer:The two triangles shown are similar - Junior Cycle Mathematics - Question 1 - 2013

Step 1

Set up the proportion based on similar triangles

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Answer

Since the triangles are similar, the corresponding sides are proportional. Therefore, we can set up the proportion:

$\frac{x}{6} = \frac{25}{15}$

Step 2

Cross-multiply to solve for x

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Answer

We can cross-multiply to find x:

$15x = 25 \times 6$

Calculating the right side gives:

$15x = 150$

Step 3

Isolate x

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Answer

Next, divide both sides by 15 to solve for x:

$x = \frac{150}{15} = 10$

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