Question

What is the value of x? Round to the nearest tenth, if necessary. X = 4 x = 5 x = 6. 2 x = 9. 4.

Answer 1

You can use the Pythagoras theorem to get the value of x.

The value of x is given by

Option C: x = 6.2

What is Pythagoras theorem?

The Pythagoras theorem:

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:

$|AC|^2 = |AB|^2 + |BC|^2$

Using the above theorem to find the value of x for the given figure

Refer to the figure attached below.

The triangle BAD is right angled triangle (one angle is 90 degrees).

The length of CD is 13 - x units.

Thus, we have:

$|AD|^2 + |DB|^2= |AB|^2\\\\Length(AD)= \sqrt{169-81} = \sqrt{88} = 2\sqrt{22}$

For triangle ACD, we have:

$|AC|^2 +|CD|^2 = |AD|^2\\|AC| = \sqrt{(2\sqrt{22})^2 - (13-x)^2} = \sqrt{-81 -x^2 - 26x}$

For triangle ACB, we have;

$|AB|^2 = |AC|^2 + |CB|^2\\81 = (-81-x^2 +26x) + x^2\\\\x = \dfrac{162}{26} = \dfrac{81}{13} \rm \: units \approx 6.2 \: \rm units$

Thus,

The value of x is given by

Option C: x = 6.2

Learn more about Pythagoras theorem here:

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