Question

3. Consider the following diagram.

f + 3g
39 - 4
15
Find the values of f and g that prove the two triangles are congruent by
the HL Theorem.

Answer 1

• g = 19/6
• f = 11/2

Explanation:

We know that:

• f + 3g = 15
• 3g - 4 = f
• Both the sides are equal because we know that both triangles are congruent.

Work:

• f + 3g = 15
• => 3g - 4 + 3g = 15
• => 6g - 4 = 15
• => 6g = 15 + 4
• => 6g = 19
• => g = 19/6
• => 3g - 4 = f
• => 3(19/6) - 4 = f
• => 19/2 - 4 = f
• => 19/2 - 8/2 = f
• => 11/2 = f

Check:

• {(f + 3g)² = f² + x²} = {15² = (3g - 4)² + x²}
• => {(11/2 + 19/2)² = 11/2² + x²} = {15² = (19/2 - 4)² + x²}
• => {(30/2)² = 11/2² + x²} = {15² = (19/2 - 8/2)² + x²}
• => {15² = 11/2² + x²} = {15² = 11/2² + x²}

Since both of them are equal, this proves that we are correct.