What is the value of x?
Enter your answer as a decimal.
2 answers:
<h3>
Answer: 42.9 </h3>
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:
42.9
Step-by-step 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
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