Answer:
The value of x is 12
Step-by-step explanation:
* Lets talk about the equilateral triangle
- The three sides of the triangle are equal in length
- The three angles of the triangle are equal in measure
- To find the measure of each one divide the sum of the measures
of the angles of the triangle by 3
∵ The sum of the measure of the angles in any triangle = 180°
∴ The measure of each angle in the equilateral Δ = 180° ÷ 3 = 60°
* Now lets solve the problem
- From the figure the three angles have the same mark, that means
the three angles are equal in measure
∵ m∠A = m∠B = m∠C
∴ Δ ABC is equilateral triangle
∴ AB = BC = AC
- WE can use any two sides of them to find the value of x
∵ AB = 4x - 10
∵ BC = 3x + 2
∵ AB = BC
∴ 4x - 10 = 3x + 2 ⇒ add 10 and subtract 3x from both sides
∴ 4x - 3x = 2 + 10 ⇒ add the like terms
∴ x = 12
- To check the answer substitute the value of x in the 3 sides to
find the length of each side (they must have the same length)
∵ AB = 4x - 10
∴ AB = 4(12) - 10 = 48 - 10 = 38 units
∵ BC = 3x + 2
∴ AB = 3(12) + 2 = 36 + 2 = 38 units
∵ AC = 5x - 22
∴ AB = 5(12) - 22 = 60 - 22 = 38 units
- All the sides are equal, then the value of x is right
* The value of x is 12
