Question

Stiind ca triunghiurile sunt asemenea si c= 5 calculati lungimea laturilor indicate

a=?
b=?
c=?

Answer 1

`a = 8 \\ b = 10 \\ c = 5`

Explanation:

`{c}^(2) = {3}^(2) + {4}^(2) \\ c = 5 \\ (3)/(6) = (4)/(a) = (5)/(b) \\ a = 8 \: \: \: \: \: b = 10`

Answer 2

`a=8\\b=10\\c=5`

Explanation:

In the given image, you can observe we have two right triangles.

Also, we know by given that those triangles are similar, which means their sides are proportional and their angles are congruent.

If the triangles are similar, we can define the following proportion between sides.

`(4)/(a) =(3)/(6)\\ 24=3a\\a=(24)/(3)\\ a=8`

Now we use the Pythagorean's Theorem to find each hypothenuse.

`c^(2) =4^(2) +3^(2)\\ c=√(16+9)=√(25) \\ c=5`

`b^(2) =8^(2) +6^(2)\\ b=√(64+36)=√(100)\\ b=10`

Therefore, the missing sides are

`a=8\\b=10\\c=5`