The vertices of a right triangle are (3, 2), (5, 3), and (5, y). what is the value of y? 3 2 3 5

  y = 2  or  -2

Step-by-step explanation:

We can take the given points to define a leg or the hypotenuse. If they define one leg of the triangle, the other leg is perpendicular at (3, 2) and intersects x=5 at y = -2.

If the given points define the hypotenuse, then one leg is along the line x=5, and the other leg meets it at y = 2.

Among the answer choices, the latter is the only one present: y = 2.

7

step-by-step explanation:

the answer would be 7

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240