Question

I need help on this question

Answer 1

4 is the correct answer

Answer 2

4

Explanation:

So, we know that these two triangles have similar angles, since they both are right triangles, but we dont know what the ratio of side lengths are.

Lets compare them:

The hypotenuse for the smaller right triangle is 2.5

The hypotenuse for the larger right triangle is 5

This is a ratio of 2.5 : 5 Or 1 : 2

If we use this ratio to find x, we get 4.

This is because the same side length for x is the opposite side length.

In this case the opposite side length for the samller triangle is 2.

So if we plug that into the 1 : 2 ratio, wiht the 1 ratio being the smaller traingle, that had the value of 2, we get 4 for x.

Can we check this? Yup.

We can use the pythagreons theorm since we know two of the sides, and they are both rigth triangles.

Pythagreons theorm is
`a^2+b^2=C^2`. a and b are the opposite and adjacent sides, while C is the hypotenuse(longest side that goes on a slant)

So lets start with the smaller triangle:

`2^2+a^b=2.5^2`

=

`4+b^2=6.25`

=

`b^2=2.25`

=

`b=1.5`

So this is the missing side length, the adjacent side length.

If we use the ratio we found above, which was 1 : 2, we should get 3 as the other triangle's adhacent side length.

Lets plug in the 5 and 4(x value) for the other triangle and see what we get:

`4^2+b^2=5^2`

=

`16+b^2=25`

=

`b^2=9`

=

`b=3`

So we got 3 for the adjacent side, and with the ratio we used to find x, got the correct answer for both the missing side, and x.

This means our answer is correct.

Hope this helps!