Question

Can you please help?

Answer 1

Answer:

$\huge\boxed{3.873}$

Step-by-step 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 $\sqrt{25}$ and $\sqrt{10}$.

Since we know the hypotenuse is $\sqrt{25}$ and one of the legs is $\sqrt{10}$, 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

$a^2 + \sqrt{10}^2 = \sqrt{25}^2$

Squaring a square root is the same as doing nothing.

$a^2 + 10 = 25\\\\a^2 = 25-10\\\\a^2 = 15\\\\a = \sqrt{15}\\\\a \approx 3.873$

Hope this helped!