Question

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

Answer 1

Answer:

(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