if f,g and h are midpoints of the sides of the triangle jkl, fg=40, kl=52 and gh=26, find each measure

Mathematics

1 answer:

vredina [299]2 years ago

7 0

Answer: The measure of JK is 60 and the correct option is d.

Explanation:

It is given that the points F, G, and H are the midpoints of the sides of triangle JKL , FG = 37, KL = 48, and GH = 30.

The point F is midpoint of JK, point G is midpoint of KL and the point H is midpoint of LJ as shown in figure .

According to the midpoint theorem, the line connecting the midpoints of two sides is parallel to the third and its length is half of the third side.

By midpoint theorem,

Therefore the measure of JK is 60 and the correct option is d.

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The "form factor" I use for this is ...

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<em>Additional comment</em>

In this expression, 'a' and 'b' are the two shortest sides (in no particular order) and 'c' is the longest side. The interpretation is ...

negative — obtuse

zero — right

positive — acute

If you're familiar with Pythagorean triples, you know that the 3-4-5 right triangle triple can be doubled to give 6-8-10. The long side of 11 is longer than the hypotenuse for the right triangle, so would correspond to a largest angle greater than 90°. The 6-8-11 triangle would be OBTUSE.