Question

What is the value of x?
Enter your answer as a decimal.

Answer 1

Answer: 42.9

There are two triangles: triangle MAB and triangle MNP

The slanted sides on the right side of the triangles are MB and MP. They correspond to one another. So they form a ratio MB/MP. I have the smaller piece up top. So we'll have the smaller piece of MAB's other known side which is MA = 35.2 (subtract 67.22 and 32) and we'll divide MA over MN = 67.2 making the ratio MA/MN

Solve the proportion for x

MB/MP = MA/MN

x/81.9 = 35.2/67.2

67.2*x = 81.9*35.2 <<--- cross multiply

67.2*x = 2882.88

x = 2882.88/67.2 <<--- divide both sides by 67.2

x = 42.9

Answer 2

42.9

Explanation:

Remark

When lines are parallel and they are cut by a transversal, their corresponding angles are equal.

• <MAB = <MNP Corresponding Angles are equal
• <MBA = <MPN Corresponding Angles are equal
• <M = <M Reflexive Property: an angle equals itself
• These Triangles are similar by AAA

Therefore Corresponding Sides of Similar Triangles are in a ratio

Equation

MA / MN = MB/MP

Givens

• MA = 67.2 - 32 = 35.2
• MN = 67.2
• MB = x
• MP - 81.9

Solution

35.2/67.2 = x / 81.9 Cross Multiply

35.2 * 81.9 = 67.2 * x Combine the left

2883 = 67.2 * x Divide by 67.2

2883/67.2 = x

x = 42.9 Answer