Question

2) Find the length of BC.
A) 12
B) 14
C) 26
D) 40

Answer 1

• 2x+3x+5=40
• 5x+5=40
• 5x=35
• x=7

BC

• 3(7)+5
• 21+5
• 26

Answer 2

Option C

Explanation:

As we can see here, the sum of AB and BC is equivalent to AC. Therefore, we obtained the following equation.

• ⇒ AB + BC = AC

We are given the following measures:

• AB = 2x
• BC = 3x + 5
• AC = 40

When we plug the values into the equation, we get;

• ⇒ 2x + 3x + 5 = 40

To determine the length of BC, we need to determine the measure of "x". This can be done by simplifying the equation obtained above. Once we determined the value of "x", we can plug the value of "x" into the expression that represents the length of BC (3x + 5) to obtain the length of BC.

• ⇒ 2x + 3x + 5 = 40
• ⇒ 5x + 5 = 40 (Collect like terms)
• ⇒ 5x + 5 - 5 = 40 - 5 (Subtract 5 both sides)
• ⇒ 5x = 35 (Simplify both sides)
• ⇒ 5x/5 = 35/5 (Divide 5 both sides)
• ⇒ x = 7 (Simplify both sides)

As stated above, let's substitute the value of "x" into the expression of BC.

• ⇒ BC = 3x + 5
• ⇒ BC = 3(7) + 5
• ⇒ BC = 21 + 5 = 26 units

Therefore, Option C is correct.