Answer:
![\huge\boxed{3.873}](https://img.qammunity.org/2021/formulas/mathematics/high-school/n597pp2g6y8as9l9l2a0b9pb2qp0hgq6rs.png)
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
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
and
.
Since we know the hypotenuse is
and one of the legs is
, we can use the Pythagorean Theorem to find the missing side.
The Pythagorean Theorem states that
, 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](https://img.qammunity.org/2021/formulas/mathematics/high-school/xlg3ib5pm1n9uanobop8qrxuc6n7ieemv5.png)
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](https://img.qammunity.org/2021/formulas/mathematics/high-school/akroknuqbwy2q1mf24ut0kuxj26xbq8poe.png)
Hope this helped!