# The figure shows three right triangles. Triangles JKM, KLM, and JLK are similar. Theorem: If two triangles are similar, the corresponding sides are in proportion. Figure shows triangle JKL with right angle at K. Segment JK is 6 and segment KL is 8. Point M is on segment JL and angles KMJ and KML are right angles. Using the given theorem, which two statements help to prove that if segment JL is x, then x2 = 100? Segment JL • segment JM = 64 Segment JL • segment ML = 48 Segment JL • segment JM = 48 Segment JL • segment ML = 36 Segment JL • segment JM = 64 Segment JL • segment ML = 36 Segment JL • segment JM = 36 Segment JL • segment ML = 64

(Segment JL)(Segment ML)=10(6.4)=64 units

Step-by-step explanation:

In the given information, triangle JKL with right angle at K. Segment JK is 6 and segment KL is 8. Point M is on segment JL and angles KMJ and KML are right angles.

we have to choose the correct option.

In order to choose we have to find the segment ML

Let ML=x therefore JM=10-m

In triangle JMK, by Pythagoras theorem

JK^{2}=JM^{2}+MK^{2}\\  36=(10-m)^2+KM^2\\KM^2=36-(10-m)^2

In triangle KML

KL^{2}=KM^{2}+ML^{2}\\  64=m^2+KM^2\\KM^2=64-m^2

From above two equations we get

36-(10-m)^2=64-m^2

⇒ 64-m^2=36-(10-m)^2

⇒ 20m=\frac{128}{20}

⇒ m=6.4 units

(Segment JL)(Segment ML)=10(6.4)=64 units

Hence, last option is correct

Segment JL × segment JM = 36

Segment JL × segment LM = 64

Step-by-step explanation:

I'm smart.

. The two statements that help to prove that if segment JL is x, then x2 = 100 are: Segment JL • segment JM = 64 and Segment JL • segment ML = 48. These two statements help to prove that if segment JL is x, then x2 = 100 because if the corresponding sides of the similar triangles are in proportion, then the ratio of the lengths of the sides is equal to the square of the ratio of the segments. Since the ratio of the segments JK : KL is 6 : 8, this means that the ratio of any segment of triangle JKL to the corresponding segment of triangle KLM is equal to the square of the ratio of 6 : 8, or 36 : 64. So if segment JL is x, then the ratio of x to the corresponding segment (JM or ML) is equal to 36 : 64 and x2 = 100.

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