Question

PLEASE ANSWER ASAP TY

In triangle ABC below, BD is the altitude. Find the length of DC. Leave your answer in
simplified radical form.

Answer 1

Explanation:

Step 1: Find AB Use Pythagoras Theorem

AB =
`\sqrt{AC^(2) -BC^(2) } = \sqrt{12^(2) -8^(2) } = √(80)`

Step 2: Find the Area of the triangle ABC

Area =
`(1)/(2)AB.BC = (1)/(2)√(80).8 = 4√(80)` =
`16√(5)`

Step 3: Find BD. Use the area of the triangle above

Area =
`(1)/(2)BD.AC`

We already known the Area and AC so, we just plug all the number in

BD =
`(2. Area)/(AC)` =
`(2.16√(5))/(12)` =
`(8√(5))/(3)`

Step 4: Find DC. Use Pythagoras Theorem of the triangle BDC

DC =
`\sqrt{BC^(2)-BD^(2) }` =
`\sqrt{8^(2)-((8√(5))/(3))^(2)}` =
`(16)/(3)`