Question

Given triangle ABC.

In blank 1, give the value of x. Just the number.

In blank 2, give the length of side AC. Just the number.

Question 1 options:
Blank # 1
Blank # 2

Answer 1

The given triangle ABC has angles A and C equal, implying AB = BC. Solving the equation 6x - 9 = 4x + 7, we find x = 8. Substituting x into AC's expression 5x - 12 yields AC = 28 units.

We are given a triangle ABC where angle A = angle C AC = 5x - 12 BC = 4x + 7 AB = 6x-9.

Now we know that if 2 angles are equal then their opposite sides are also equal in measure.

So,

AB = BC

6x - 9 = 4x + 7

Rearranging the equation

6x - 4x = 7 + 9

2x = 16

x = 8

So , the value of x is 8.

Now , we need to find the value of side AC.

As we have already taken out the value of x we can substitute it in 5x - 12

So ,

5(8) - 12

40-12

28 units

So , the value of AC = 28 units.