Question

What is the PERIMETER of triangle ABC ?

45 POINTS!

(A) 12 units

(B) 13 units

(C) 14 units

(D) 18 units

Answer 1

Answer: The correct option is (D) 18 units.

Step-by-step explanation: We are given to find the perimeter of triangle ABC.

As shown in the attached figure below, triangle ABC is divided into two right-angled triangles ABD and ACD.

From the figure, we note that

AC = 8 units.

And the side lengths AB and BC are calculated using Pythagoras theorem of right-angled triangles as follows :

`AB=√(AD^2+BD^2)=√(3^2+4^2)=√(25)=5~\textup{units},\\\\BC=√(CD^2+BD^2)=√(3^2+4^2)=√(25)=5~\textup{units}.`

We know that the perimeter of a triangle is equal to the sum of the lengths of the three sides.

Therefore, the required PERIMETER of ΔABC is given by

`P=AB+BC+AC=5+5+8=18~\textup{units}.`

Thus, the perimeter of ΔABC is 18 units.

Option (D) is CORRECT.

Answer 2

The length of AC is 8

The length of 1/2 of AC = 4 (set the "4" point as D)
DC = 4

DC = 4,DB = 3, CB = x

Use the pythagoream theorem.

4² + 3² = x²
16 + 9 = x²
25 = x²

root both sides to isolate the x
√25 = √x²
x = √25
x, or CB = 5

Add all the sides together. Remember, CB = 5, DC = 4, & DB = 3
5 + 4 + 3 = 12

12, or (A) is your answer

hope this helps