Question

Find j.

'T
j
45°
22 km
45°
Write your answer in simplest radical form.
kilometers

Answer 1

`11\sqrt2 \text{ km}`

Explanation:

We can solve for j by using our knowledge of 45-45-90 triangles.

• the legs are congruent

• the hypotenuse is
`\sqrt2` times the length of the legs

We can use that second fact to solve for j. Since j is a leg, we can divide the hypotenuse (22 km) by
`\sqrt2` to solve for it.

`j = (22)/(\sqrt2)`

Now, we can rationalize j by multiplying by
`(\sqrt2)/(\sqrt2)`.

`j = (22)/(\sqrt2) \cdot (\sqrt2)/(\sqrt2)`

`\boxed{j = 11\sqrt2 \text{ km}}`