Question

If the following triangles are similar, find the value of x.

a) x = 3
b) x = 4
c) x = 5
d) x = 6

Answer 1

To find the value of x, we can set up a proportion using the ratios of the corresponding sides of the similar triangles.

Step-by-step explanation:

To find the value of x in the given similar triangles, we need to compare corresponding sides of the triangles. If all three triangles are similar, then the ratios of corresponding sides should be equal.

Let's compare the sides:

In triangle ABC, the ratio of BC to AC is 4/3.

In triangle DEF, the ratio of EF to DF is (6 + x)/6.

Setting up the proportion, we have (6 + x)/6 = 4/3.

Cross-multiplying, we get 3(6 + x) = 4(6).

Simplifying the equation, we have 18 + 3x = 24.

Subtracting 18 from both sides, we get 3x = 6.

Dividing by 3, we find that x = 2.