Question

Find the value of x. If your answer is not an integer, leave it in simplest radical form. The diagram is not drawn to scale.

Answer 1

The value of x is 5√3.

Explanation:

From the given figure it is clear that it is a right angled triangle. The length of legs are 5 units and x units. The length of hypotenuse is 10 units.

According to the Pythagoras theorem, the sum of squares of two legs of a right angled triangle is equal to the square of its hypotenuse.

`leg_1^2+leg_2^2=hypotenuse^2`

Substitute leg₁ = 5, leg₂ = x and hypotenuse = 10 in the above formula.

`(5)^2+x^2=(10)^2`

`25+x^2=100`

Subtract 25 from both the sides.

`25+x^2-25=100-25`

`x^2=75`

Taking square root both the sides.

`x=√(75)`

`x=5√(3)`

Therefore the value of x is 5√3.

Answer 2

Using the Pythagorean theorem:

10^2 = 5^2 +x^2

100 = 25 + x^2

x^2 = 100-25

x^2 = 75

x = √75 = 5√3