Altitude-on-hypotenuse

Find the value of x x 4√3 10 x = 4√3 4√3 x + 10 x x = 163 x x – 48 = 0 (x – 4)(x + 12) = 0 x = 4 x = -12

Find the value of x x j 9 j = 6 6 j + 9 j 2 + 9x = 36 j 2 + 9x – 36 = 0 (j – 3)(j + 12) = 0 j = 3 j = = x x 9 x 2 = 27 x = 3√3

Find the value of x x 4√3 5√3 4√3 = x x 5√3 x 2 = 203 x 2 = 60 x = 2√15

Find the value of x x = x x 15 x 2 = 180 x = 6√5

Find the value of x x 4√5 8 x + 8 = 4√5 4√5 8 8x + 64 = 165 8x + 64 = 80 8x = 16 x = 2

Pythagorean Thm and Converse

Find the value of x x 4√ (4√3) 2 = x = x 2 x 2 = 148 x = 2√37

Find the value of x x x 2 = x 2 =676 x 2 = 576 x = 24

Do the following sides lengths form an acute, right, or obtuse triangle? 25, 24, ? = 625 right

Do the following sides lengths form an acute, right, or obtuse triangle? 12, 13, ? > 225 acute

Do the following sides lengths form an acute, right, or obtuse triangle? 32, 35, ? < 4096 obtuse

Radicals

Simplify the radical expression. √200 + √ √8 10 √2 + 5 √ √2 10 √2 + 5 √2 + 6 √2 21 √2

Simplify the radical expression. 4√12 + 5√72 + 8√ √ √ √3 8√3 + 30√2 + 56√3 30√2 + 64√3

Simplify the radical expression. 8 √6 3 √ √2 = 72 √2 = 36 √

Simplify the radical expression. √200 5 √3 10 √2 √3 2 √6 = 2 √6 5 √3 √3 5315

Simplify the radical expression. 6√5 9√3 2√5 √3 2√15 = 2 √15 3√3 √3 33 9