[list=1][*][b]Step 1:[/b] The 'hypotenuse square' is composed of one larger square take away four identical right triangles. [b]Step 2:[/b] [math]A=13^2-4\left[\frac{1}{2}\left(8\cdot5\right)\right]=169-4\left[\frac{1}{2}\left(40\right)\right]=169-4\left[20\right]=169-80=89[/math] units[sup]2[/sup]. [b]Step 3:[/b] [math]l=\sqrt{89}\cong9.43[/math] units.[/*][*][b]Step 1:[/b] The 'hypotenuse square' is composed of one smaller square and four identical right triangles. [b]Step 2:[/b] [math]A=3^2+4\left[\frac{1}{2}\left(6\cdot3\right)\right]=9+4\left[\frac{1}{2}\left(18\right)\right]=9+4\left[9\right]=9+36=45[/math] units[sup]2[/sup]. [b]Step 3:[/b] [math]l=\sqrt{45}\cong6.71[/math] units.[/*][/list]

[list=1][*]9, 16, and 25 units[sup]2[/sup] (9+16=25)[/*][*]25, 144, and 169 units[sup]2[/sup] (25+144=169)[/*][*]36, 64, and 100 units[sup]2[/sup] (36+64=100)[/*][/list]The two smaller square areas add up to the larger square area.[br][br][b][color=#1e84cc]Bonus:[/color][/b] The squares of each leg add up to the square of the hypotenuse.

For the squares made by the sides of a right triangle, the areas of the two smaller squares (made by the legs) make up the area of the larger square (made by the hypotenuse).

[list=1][*][math]c^2=a^2+b^2=1^2+7^2=1+49=50[/math] units[sup]2[/sup], [b]c[sup]2[/sup] = 50 units[sup]2[/sup][/b], and [math]c=\sqrt{50}\cong7.07[/math] units, [b]c = 7.07 units[/b][/*][*][math]c^2=a^2+b^2=9^2+4^2=81+16=97[/math] units[sup]2[/sup], [b]c[sup]2[/sup] = 97 units[sup]2[/sup][/b], and [math]c=\sqrt{97}\cong9.85[/math] units, [b]c = 9.85 units[/b][/*][/list][b][center][color=#ff0000]Don't forget to take the square root of c[sup]2[/sup] to find c![/color][/center][/b]