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In the figure below, the perimeter of the triangle is 12 + 4√3 inches. What is the value of x, in inches?
- a)2
- b)4
- c)6
- d)8
- e)12
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
In the figure below, the perimeter of the triangle is 12 + 4&rad...
The correct answer is B. To solve this problem, recognize that the triangle is a “special triangle.” A right triangle in which the length of the longer leg is √3 times the length of the shorter leg is a 30◦ −60◦ −90◦ right triangle. Another property of this type of right triangle is that the hypotenuse is 2 times the length of the shorter leg. So, this right triangle has lengths x, x√3, and 2x. The perimeter is the sum of the lengths of the sides. You are given that the perimeter equals 12 + 4√3. Set the two equations equal and solve for x:
12 + 4√3 = x + x√3 + 2x
12 + 4√3 = 3x + x√3
For the right side of the equation to equal the left side of the equation, x must be equal to 4.
12 + 4√3 = x + x√3 + 2x
12 + 4√3 = 3x + x√3
For the right side of the equation to equal the left side of the equation, x must be equal to 4.
Most Upvoted Answer
In the figure below, the perimeter of the triangle is 12 + 4&rad...
The correct answer is B. To solve this problem, recognize that the triangle is a “special triangle.” A right triangle in which the length of the longer leg is √3 times the length of the shorter leg is a 30◦ −60◦ −90◦ right triangle. Another property of this type of right triangle is that the hypotenuse is 2 times the length of the shorter leg. So, this right triangle has lengths x, x√3, and 2x. The perimeter is the sum of the lengths of the sides. You are given that the perimeter equals 12 + 4√3. Set the two equations equal and solve for x:
12 + 4√3 = x + x√3 + 2x
12 + 4√3 = 3x + x√3
For the right side of the equation to equal the left side of the equation, x must be equal to 4.
12 + 4√3 = x + x√3 + 2x
12 + 4√3 = 3x + x√3
For the right side of the equation to equal the left side of the equation, x must be equal to 4.
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In the figure below, the perimeter of the triangle is 12 + 4√3 inches. What is the value of x, in inches?a)2b)4c)6d)8e)12Correct answer is option 'B'. Can you explain this answer?
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