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Point L is on line segment start overline, K, M, end overline KM . Given K, M, equals, 5, x, plus, 10, commaKM=5x+10, L, M, equals, 4, x, commaLM=4x, and K, L, equals, 3, x, commaKL=3x, determine the numerical length of start overline, K, L, end overline, . KL .

Question

Point L is on line segment start overline, K, M, end overline KM . Given K, M, equals, 5, x, plus, 10, commaKM=5x+10, L, M, equals, 4, x, commaLM=4x, and K, L, equals, 3, x, commaKL=3x, determine the numerical length of start overline, K, L, end overline, . KL .

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Solution

Given that point L is on line segment KM, we can say that KM = KL + LM.

We know that KM = 5x + 10, KL = 3x, and LM = 4x.

Substituting KL and LM into the equation, we get:

5x + 10 = 3x + 4x 5x + 10 = 7x 10 = 2x x = 5

Substitute x = 5 into KL = 3x to find the length of KL:

KL = 3(5) = 15

So, the numerical length of KL is 15.

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