Question

Ion know how to do this and im tired i need help please

Answer 1

B. x = 8√7, y = 4√21

Explanation:

Look at the largest right triangle so the hypotenuse equals 12 + 16 = 28

According to the Pythagorean Theorem: y^2 + x^2 = 28^2

Then for the 2 smaller right triangles, they all the the same side, just called it z

so y^2 = 12^2 + z^2 => z^2 = y^2 - 12^2

and x^2 = 16^2 + z^2 => z^2 = x^2 - 16^2

then y^2 - 12^2 = x^2 - 16^2

y^2 - 144 = x^2 - 256

y^2 = x^2 - 112

Using the first equation

y^2 + x^2 = 28^2 => x^2 = 784 - y^2

So we have y^2 = x^2 - 112

and x^2 = 784 - y^2

then y^2 = (784 - y^2) - 112

y^2 + y^2 = 784 - 112

2y^2 = 672

y^2 = 336

y = 4√21

x^2 = 784 - y^2 = 784 - 336 = 448

x = 8√7

Answer 2

To solve this, you can use the geometric mean theorem. The leg of a right triangle is the geometric mean between the hypotenuse and the portion of the hypotenuse adjacent to the leg.

So that means that 28/y = y/12. You can then use means and extremes of proportions to simplify, and you get y^2 = 336, a.k.a y = 4 root 21.

Then you do the same thing but with x.

28/x = x/16

x^2 = 448

x = 8 root 7