If the hypotenuse of a right triangle has length 9 feet and one of the other sides has length 2 feet, what is the length of the remaining side, in feet? \sf A) √(11) \sf B) √(7)…

Question

If the hypotenuse of a right triangle has length 9 feet and one of the other sides has length 2 feet, what is the length of the remaining side, in feet?


`\sf A) √(11)`

`\sf B) √(7)`

`\sf C) √(85)`

`\sf D) √(77)`

`\sf E) 7`

Answer 1

• Hypotenuse=H=9ft
• Base=B=2ft

Apply Pythagorean theorem

• P²=H²-B²
• P²=9²-2²
• P²=81-4
• P²=77
• P=√77

Option D

Answer 2

`\sf D) √(77) \: ft`

Explanation:

Given that,

→ Perpendicular (x) = ?

→ Hypotenuse (h) = 9 feet

→ Base (b) = 2 feet

Now by using the Phythagoras theorem,

→ (Hypotenuse)² = (Perpendicular)² + (Base)²

→ (h)² = (x)² + (b)²

→ (9)² = (x)² + (2)²

→ 81 = (x)² + 4

→ (x)² = 81 - 4

→ (x)² = 77

→ [ x = √(77) ]

Thus, length of remaining side is √(77) ft.