The triangles shown are similar.
What is the value of x?
Two similar triangles, one triangle has legs 3 units and 4 units and hypotenuse of 5 units, another triangle has legs 9 units and 12 units and hypotenuse of unknown units.
Question 3 options:
20
12
13
15
Since the triangles are similar, their corresponding sides must be proportional.
In the first triangle, the ratio of the lengths of the legs is 3:4. In the second triangle, the lengths of the legs are 9:12, which simplifies to 3:4 as well.
Similarly, the ratio of the length of the hypotenuses is 5:x.
We can set up a proportion to find the value of x:
3/4 = 5/x
Cross-multiplying, we get:
3x = 20
Dividing both sides by 3, we get:
x = 20/3
Therefore, the value of x is approximately 6.67.
None of the given answer options match this value, so none of them are correct.