Question

What is the length of Line segment B C, rounded to the nearest tenth? 13. 0 units 28. 8 units 31. 2 units 33. 8 units.

Answer 1

The length of the line segment BC is 31.2 units.

Given that

Triangle ABC is shown.

Angle ABC is a right angle.

An altitude is drawn from point B to point D on side AC to form a right angle.

The length of AD is 5 and the length of BD is 12.

We have to determine

What is the length of Line segment BC?

According to the question

The altitude of the triangle is given by;

$\rm Altitude = \sqrt{xy}$

Where x is DC and y is 5 units.

Then,

The length DC is.

$\rm Altitude = \sqrt{xy}\\ \\ 12 = \sqrt{(DC) \times 5}\\ \\ \sqrt{DC } = \dfrac{12}{\sqrt{5}}$

Squaring on both sides

$\rm DC = \dfrac{144}{5}\\ \\ DC = 28.8$

Considering right triangle BDC, use the Pythagorean theorem to find BC:

$\rm BC^2 = DC^2+BD^2\\\\ BC^2 = (28.8)^2+(12)^2\\ \\ BC = \sqrt{829.44+144}\\ \\ BC = \sqrt{973.44}\\ \\ \rm BC = 31.2 \ units$

Hence, the length of the line segment BC is 31.2 units.

To know more about Pythagoras Theorem click the link given below.

brainly.com/question/26252222