Question

Solve for x to the nearest tenth.
2
X
4
10

Answer 1

x ≈ 8.9

Explanation:

using Pythagoras' identity.

the square on the hypotenuse of a right triangle is equal to the sum of the squares on the other 2 sides.

consider the right triangle on the left with hypotenuse h , then

h² = 2² + 4² = 4 + 16 = 20 ( take square root of both sides )

h =
`√(20)`

consider the right triangle on the right , then

x² + h² = 10²

x² + (
`√(20)` )² = 10²

x² + 20 = 100 ( subtract 20 from both sides )

x² = 80 ( take square root of both sides )

x =
`√(80)` ≈ 8.9 ( to the nearest tenth )