Question

I don't understand how to do find x and y, please help? thank yous.

Answer 1

#8) There are THREE right-angle (90°) TRIANGLES.

The "big" triangle has legs "x" and "no designation - so lets call it Z" and hypotenuse "4+5" = 9

The "left" triangle has legs "4" and "y" and hypotenuse "x"

The "right" triangle has legs "5" and "y" and hypotenuse "no designation - which we named Z"

Now, you can create a system of equations - you have three unknown variables and can create an equation for each triangle using the Pythagorean Theorem.

Big: x² + Z² = 9² → x² + Z² = 81

Left: 4² + y² = x² → 16 + y² = x² → 16 = x² - y² → x² - y² = 16

Right: 5² + y² = Z² → 25 + y² = Z²

Next, let's eliminate Z by using substitution....use the Right equation to plug Z² into the Big equation to create a NEW Big equation.

NEW Big: x² + (25 + y² ) = 81 → x² + y² = 81 - 25 → x² + y² = 56

Now, we have two unknown variables (x and y) and two equations (NEW Big and Left). Solve the system using any method. I am going to solve using the elimination method)

NEW Big: x² + y² = 56

+ Left: x² - y² = 16

2x² = 72 added the NEW Big and Left equations

x² = 36 divided both sides by 2

x = 6 took square root of both sides (NOTE: -6 is disregarded because we are solving for a length, which cannot be negative)

The last step is to plug the "x" value (that we just solved for) into one of the equations to solve for "y". I am choosing to use the Left equation.

x² - y² = 16

36 - y² = 16

- y² = 16 - 36

- y² = -20

y² = 20

y = √20

y = 2√5

Answer: x = 6, y = 2√5

Try #9 on your own and then check your answers below:

Big: Z² + x² = 12², Left: 3² + y² = Z², Right: y² + 9² = x²

Answer: x = 6√3, y = 3√3