Question

What's the length of side AB in ∆ABC shown?
A. 5
B. √313
C. 6
D. √15​

Answer 1

The value of x = 5 units.

Explanation:

Given the right-angled triangle ∆ABC with the following dimensions

AC = a = 12

BC = c = hypotenuse = 13

AB = b = x

Pythagorean Theorem

For a right-angled triangle with the sides, a and b the hypotenuse c is defined as:

`c=√(a^2+b^2)`

Thus, using the Pythagorean Theorem to determine the value 'x',

`b=√(c^2-a^2)`

as b = x, so

`x=√(c^2-a^2)`

• a = 12

• c = 13

so

`x=√(13^2-12^2)`

`x=5`

Therefore, the value of x = 5 units.