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One side of a triangle is 5 units longer than a second side. The ray bisecting the angle formed by these sides divides the opposite side into segments that are 7 units and 9 units long. Find the perimeter of the triangle. Give your answer as a reduced fraction or exact decimal

Please explain your answer.

Sagot :

xero099

The perimeter of the triangle described in statement has a measure of 56 units long.

How to determine the perimeter of a triangle

After a quick though careful reading, we construct a triangle based on all information given in the statement, based on the fact that the longest segment is adjacent to the longest missing side. Since both sides have two angles with the same magnitude, then we have the following ratios:

[tex]\frac{x}{7} = \frac{x+5}{9}[/tex]   (1)

Now we solve the expression for x:

9 · x = 7 · x + 35

2 · x = 35

x = 17.5

And the perimeter of the triangle is determine by summing the three sides:

p = 9 + 7 + (17.5) + (17.5 + 5)

p = 56

The perimeter of the triangle described in statement has a measure of 56 units long. [tex]\blacksquare[/tex]

To learn more on triangles, we kindly invite to check this verified question: https://brainly.com/question/2773823

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