Question

HELP ASAP!!!!!!!! You are given an extended ratio that compares the lengths of the sides of the triangle. Find the length of each side. AC : BC : AB is 2 : 1 : 2

Answer 1

AB = 8 units, AC = 8 units, and BC = 4 units

Step-by-step explanation:

We can use the given ration of 2:1:2. We are told that AC and AB both represent 2 parts of the perimeter of the triangle, so they are equal in length.

So what we get is

AC = AB or

2x = x + 4

we can solve the above equation to find x...

2x = x + 4

x = 4 (subtract 'x' from both sides to isolate x)

Now plug in 4 to the x values to find the length if the sides for AB and AC

AC = 2x = 2(4) = 8

AB = x + 4 = 4 + 4 = 8

We are told that BC represents 1 part of the ration, so it is one half as long as the other sides, since they each represent 2 parts (1 is half of 2). Half of 8 is 4, so we have the correct values

Answer 2

AB = 8 units, AC = 8 units, and BC = 4 units

Explanation:

We can use the given ration of 2:1:2. We are told that AC and AB both represent 2 parts of the perimeter of the triangle, so they are equal in length.

So what we get is

AC = AB or

2x = x + 4

we can solve the above equation to find x...

2x = x + 4

x = 4 (subtract 'x' from both sides to isolate x)

Now plug in 4 to the x values to find the length if the sides for AB and AC

AC = 2x = 2(4) = 8

AB = x + 4 = 4 + 4 = 8

We are told that BC represents 1 part of the ration, so it is one half as long as the other sides, since they each represent 2 parts (1 is half of 2). Half of 8 is 4, so we have the correct values