Question

What is the area of the square adjacent to the third side of the triangle?

Answer 1

Answer:

85 units^2 = Area of Blue Square

and

x = 5 units

Step-by-step explanation:

To do this we use the Pythagorean theorem (a^2 + b^2 = c^2). a and b represent the legs of the triangle whereas c represents the longest side of the triangle, or the hypotenuse.

Since we know the area of a square is the side length multiplied by itself (or the side length squared), $\sqrt{35}$ is the side length of the pink square and $\sqrt{50}$ is the side length of the green square.

That means a = $\sqrt{35}$ and b = $\sqrt{50}$ , so...

$(\sqrt{35} )^{2} + (\sqrt{50})^{2} = c^{2}$

35 + 50 = c^2

85 = c^2

$\sqrt{85} = c$

Now we need to square the square root of 85 to find the area of the blue square.

$(\sqrt{85})^{2} = Area of blue square$

85 units^2 = Area of Blue Square

To solve the other question we use the same formula again.

$x^2 + 12^2 = 13^2\\x^2 +144 = 169\\-144\\x^2 = 25\\x=\sqrt{25} \\x=5$

x = 5 units