Tall hedges are shading a rose garden. At the time the gardener wants the garden to be in sunlight, a four- foot vertical pole casts a five foot shadow. Suppose that we want to cut the hedges back only to a height of 8 feet. How far must the edge of the garden be from the base of the hedge if we do not want any part of the rose garden to be in the shade?

Step-by-step explanation:

A 4-ft pole casts a 5-ft shadow, so an 8-ft hedge casts a 10-ft shadow. Tge hedges must be 10 ft from the garden.

(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