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andreev551 [17]

2 years ago

15

Triangle JKL and triangle MNP are similar.

1 answer:

Rom4ik [11]2 years ago

5 0

Answer:

Option G

Step-by-step explanation:

We know that both triangles are similar in proportion. We see that the base of 8 is similar to 6, and therefore the side length of x should be similar to 5.

x/5 = 8/6

Cross multiply.

6x = 40

x = 40/6

x = 6 + 2/3

x = 6.67

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What is the length of line segment KJ?

Karolina [17]

Please consider the attached file.

We can see that triangle JKM is a right triangle, with right angle at M. Segment KM is 6 units and segment MJ is 3 units. We can also see that KJ is hypotenuse of right triangle.

We will use Pythagoras theorem to solve for KJ as:

$KJ^2=KM^2+MJ^2$

$KJ^2=6^2+3^2$

$KJ^2=36+9$

$KJ^2=45$

Now we will take positive square root on both sides:

$\sqrt{KJ^2}=\sqrt{45}$

$KJ=\sqrt{9\cdot 5}$

$KJ=3\sqrt{5}$

Therefore, the length of line segment KJ is $3\sqrt{5}$ and option D is the correct choice.

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Hello!

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