Question

Find the unknown side length, x.

Answer 1

√65 = x; using the Pythagorean Theorem, 25 [hypotenuse₁] - 9 [short leg₁] = 16 [long leg₁]. Take the square root of 16 to get 4 [reflexive line where the two triangles meet]. Then, you deal with the larger triangle. You have 16 [short leg₂] + 49 [long leg₂] = 65 [hypotenuse₂]. Finally, take the square root of 65, so long it stays √65. There is no perfect square to find that will simplify that 65 inside that radical.

Answer 2

B. √65

Explanation:

Use the Pythagorean theorem for both triangles.

Let y be the common side of the triangles. Therefore:

y² + 3² = 5²

y² + 9 = 25 subtract 9 from both sides

y² = 16

x² = 7² + y²

x² = 49 + 16

x² = 65 ⇒ x = √65