Question

Find the value of x in the triangle shown below.

Answer 1

x = 8

Explanation:

According to Pythagorean Theorem

`AB {}^(2) + BC {}^(2) = AC {}^(2)`

here

`AB = x \\ BC = 6 \\ AC = 10`

Now,

`{x}^(2) + {6}^(2) = 10 {}^(2) \\ {x}^(2) = {10}^(2) - {6}^(2) \\ x {}^(2) = 100 - 36 \\ {x}^(2) = 64 \\ x = √(64) \\ x = 8`

AB = x = 8

Answer 2

x=8

Explanation:

We can use the Pythagorean theorem to solve

a^2+b^2 = c^2 where a and b are the legs and c is the hypotenuse

6^2 + x^2 = 10^2

36 + x^2 = 100

Subtract 36 from each side

36-36 +x^2 = 100-36

x^2 = 64

Take the square root of each side

sqrt(x^2) = sqrt(64)

x = 8