Question

What is the length of EF in the right triangle below?

Answer 1

`√(120)`

Explanation:

We can use the Pythagorean Theorem to solve this question.

The Pythagorean Theorem:
`a^2+b^2=c^2`, where a and b are the lengths, and c is the hypotenuse.

Using the image, we can write the equation:
`13^2+b^2=17^2`.

Simplify:
`169+b^2=289`.

Subtract 169 on both sides, we can know that
`b^2=120`.

Square root on both sides, we can get b =
`√(120)`.

Hope this helps!

Answer 2

EF =
`√(120)`

Explanation:

Since this triangle is right, we can use the pythagorean theorem to find the missing side length. The pythagorean theorem states that the square of the hypotenuse(DE) is equal to the sum of the squares on the legs(DF, EF). We can write:

DE^2 = DF^2 + EF^2

and substitute the values:

17^2 = 13^3 + EF^2

289 = 169 + EF^2

EF^2 = 120

EF =
`√(120)`