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What is the value for x?

What is the value for x?-example-1
User Shantr
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2 Answers

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Answer:

x = 12

Explanation:

Since all 3 angles are congruent then the triangle is equilateral, thus all 3 sides are also congruent.

Equate any 2 of the sides and solve for x

5x - 22 = 3x + 2 ( subtract 3x from both sides )

2x - 22 = 2 ( add 22 to both sides )

2x = 24 ( divide both sides by 2 )

x = 12

User IgorGIS
by
8.7k points
1 vote

Answer:

The value of x is 12

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

User Sherwin Yu
by
7.9k points

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