Question

Find the value of x. Leave your answer in simplest radical form.

Answer 1

Explanation:

Pythagoras.

c² = a² + b²

c being the Hypotenuse (the side opposite of the right angle).

so, the length of the rectangle is the Hypotenuse of the right-angled triangle on the top :

length² = 7² + 3² = 49 + 9 = 58

length = sqrt(58)

the diagonal of the rectangle is again the Hypotenuse of the right-angled triangle of length (sqrt(58)), width (x) and diagonal (9) of the rectangle.

so, we have

9² = sqrt(58)² + x² = 58 + x²

81 = 58 + x²

23 = x²

x = sqrt(23)

Answer 2

First you need to find at least two dimensions of the triangle containing a side length of x. The triangle of the top can be used for that. The hypothenuse for the 7,3 triangle is
`√(58)`.

Now we can use the other triangle with sides of x,
`√(58)`, and a hypothenuse of 9 to find x.

x^2 +
`√(58)^2` = 9^2

simplify

x^2 + 58 = 81

subtract 58 from both sides

x^2 = 23

x =
`√(23\\)`

and since this radical cannot be simplified further that is your answer.

Explanation: