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Please help quick! Geometry! Find KL please

Please help quick! Geometry! Find KL please-example-1

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Explanation:

it is a number line with differences between numbers on the line. this is only drawn in a geometric way to actually make it easier to see. but it is not really geometry. it is about the difference between numbers, when certain differences are equal.

so, yes, the length of the whole line (the difference between the numbers H and L) is given as 32.1.

then we know the difference between J and L is 22.3.

then we know the difference between G and H is half of the difference between K and L.

due to the markings we also know that the difference between H and J is the same as between K and L (and therefore the same as twice the distance between G and H).

because of the first 2 points, we know that the difference between H and J is 32.1 - 22.3 = 9.8.

so,

HL = 32.1

JL = 22.3

HJ = KL = 32.1 - 22.3 = 9.8

GH = 1/2 KL = 1/2 HJ = 9.8/2 = 4.9

now we can say

as GH = 1/2 KL = 1/2 HJ,

GJ = GH + HJ = GH + 2GH = 3GH = 3×4.9 = 14.7

JK = HL - HJ - KL = 32.1 - 9.8 - 9.8 = 12.5

GK = GH + HJ + JK = 4.9 + 9.8 + 12.5 = 27.2

GL = GK + KL = 27.2 + 9.8 = 37.0

HK = HJ + JK = 9.8 + 12.5 = 22.3

User Thkala
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