Question

Can you please help?

Answer 1

`\huge\boxed{3.873}`

Explanation:

Note that the squares are on the sides of these triangles are on the hypotenuse/one leg.

We know that the area of a square is
`l^2` where l is the length. Since we know the area, we can find the square root of the area to find the side length.

So the side lengths are
`√(25)` and
`√(10)`.

Since we know the hypotenuse is
`√(25)` and one of the legs is
`√(10)`, we can use the Pythagorean Theorem to find the missing side.

The Pythagorean Theorem states that
`a^2 + b^2 = c^2`, where c is the hypotenuse and a/b are the legs.

We know the hypotenuse and a leg, so we can substitute inside

`a^2 + √(10)^2 = √(25)^2`

Squaring a square root is the same as doing nothing.

`a^2 + 10 = 25\\\\a^2 = 25-10\\\\a^2 = 15\\\\a = √(15)\\\\a \approx 3.873`

Hope this helped!