Step-by-step explanation:

The perimeter of a rectangular swimming pool is 86 m and its area is 450 m^2 

A. How would you represent the length and the width of the swimming pool?

B. What equation represents the perimeter of the swimming pool? How about the equation that represents its are?

C. How would you find the length and the width of the swimming pool?

D. What is the length of the swimming pool? How about its width? Explain how you arrived at your answer.

E. How would you check if the dimension of the swimming pool obtain satisfy the conditions of the given equation?

F.suppose you have the dimension of the swimming pool are both doubled, how would it affect its perimeter? How about its area? 

Hope you answer it. Thanks. 

Answer by rothauserc(4717)   (Show Source): You can put this solution on YOUR website!

Let l be the length and w be the width

Perimeter (P) = 2l + 2w

Area (A) = l * w

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A. let l be length and w be width

B. P = 2l + 2w, A = l * w

C. we have two equations in two unknowns, solve by substitution

D. we are given

1) 86 = 2l + 2w

2) 450 = l * w

consider the first equation

86 = 2l + 2w

divide both sides of = by 2

43 = l + w, then

l = 43 - w

now substitute for l in our second equation

450 = (43 - w) * w

450 = 43w - w^2

rearrange terms

w^2 - 43w + 450 = 0

factor the quadratic equation

(w - 25) * (w - 18) = 0 and

w = 25 or w = 18

note that 25 * 18 = 450 = A, therefore

choose l = 25 m and w = 18 m

E.check our dimensions with the equation for P

86 = (2 * 25) + (2 * 18)

86 = 50 + 36

86 = 86

our dimensions check

F.if we double our dimensions we have l = 50 and w = 36 then

P' = 2*50 + 2*36 = 172 therefore we double P

A' = 50 * 36 = 1800 therefore we quad-rouble (4 times) A