Question

the lgs of right triangle FGH are 12 meters and 16 meters. The shortest side of triangle JKL is 2.4 meters and triangle JKL is similar to triangle FGH. How long is the hypotenuse of triangle JKL

Answer 1

the second word is soposed to be legs

Answer 2

In general, when two figures are similar to each other, the ratio of the corresponding sides of one figure is equivalent to corresponding set of sides of the other figure.

In this case, the ratio of the legs of right triangle FGH is 12/16. That reduces to 3/4.

Since the ratio of the legs of FGH is 3/4, then there must exist an equivalent ratio for the set of legs of JKL as well.

To find the proper equivalent ratio, we simply set 3/4 = 2.4/x

In other words, we place the values for the short legs in the numerator, and the values for the longer legs in the numerator. The unknown value, we will need to find.

So cross multiplying gives 3x = 9.6

solving for x, we get x = 9.6/3

x = 3.2

Unfortunately, that only gives us the value of the longer leg of triangle JKL. We still have to find the length of the hypotenuse for that triangle. To do that use the highly popular pythagorean theorem: a^2 + b^2 = c^2 to find it. Do you believe you can do it from here?

Answer 3

yes thank you sooooooooo much, that just helped me a bunch for my test 2marow.

Answer 4

Happy to help :D

But we still haven't found the length of the hypotenuse yet. Do you believe you can find it?

Answer 5

yes i get it now thanks XD

Answer 6

ok i worked it out, is it 4?

Answer 7

That is correct. I guess you really do get it :D

Answer 8

YYAAAYYYYYYY
lol thanks so much