Given: Circle X with radius r and circle
Y with radius s
Prove: Circle X is similar to circle Y.
Stalements Reasons
translate X to Y
circle X ~ circle'Y
dilate circle X by sir
circle with center X
has radius
circle with center Y
has radius s
Reasons
1. given
Statements
✓ 1. circle with center X
has radius
✓ 2. circle with center Y
has radius s
✓ 3. translate X to Y
2. given
✓
4. dilate circle X by slr
3. translation is a
similarity transformation
4. dilation is a
similarity transformation
Demo

its 50 miles away from the starting point

(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