Question

What is the value or x?

Answer 1

x = 25

Explanation:

Since the given triangle is a right triangle and we are also given two sides which are opposite (height) = 24 units and adjacent (base ) = 7 units. We can apply the Pythagoras Theorem where:

`\displaystyle{\text{opposite}^2 + \text{adjacent}^2 = \text{hypotenuse}^2}`

In simpler words, it is:

`\displaystyle{\text{height}^2 + \text{base}^2 = \text{slope}^2}`

Substitute in given values:

`\displaystyle{24^2+7^2=x^2}`

Evaluate and solve for x:

`\displaystyle{576+49=x^2}\\\\\displaystyle{625=x^2}\\\\\displaystyle{√(625)=√(x^2)}\\\\\displaystyle{\pm √(625)=x}\\\\\displaystyle{\pm 25=x}`

However, x is a length value and length's value cannot be negative so x can only be 25.

Hence, x = 25 units