Given the picture, what is the length of ac? a) 4.5 b) 5 c) 7.5 d) 8

we know that

triangles BCD and ACE are similar

so, their ratios of sides must be equal

Calculation of y:

we can see that

AC=AB+BC

AC=y+3

CE=CD+DE

CE=4+6

CE=10

now, we can plug values

now, we can solve for y

Calculation of AC:

we know that

AC=y+3

we can plug y

and we get

...................Answer

(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

-81 -56 -27 0 81

step-by-step explanation: