To find: The dimension of the froor and the dimension of the fountain-pool area.

Daniaal Sanchez

Daniaal Sanchez

Answered question

2021-09-09

To find: The dimension of the froor and the dimension of the fountain-pool area.

Answer & Explanation

aprovard

aprovard

Skilled2021-09-10Added 94 answers

Procedure used:
And Application of a Nonlinear System:
"Step 1: Assume the variables in order to represent unknown quantities.
Step 2: Write a system of equations modeling the condition in the problem.
Step 3: Solve the system and answer the question asked in the problem.
Step 4: Check the proposed solution in the original wording of the problem."
Calculation:
It is given that the perimeter and area of the floor with the fountain-pool area removed are 24 meters and 21 square meter, respectively.
Step 1: Assume the side of floor and side fountain-pool floor to be x and y, respectively.
Step 2: Model the given conditions into a system of equations.
As the perimeter of the floor without fountain-pool area is 24 meters, it gives 4x+2y=24(3x+xy+3y=4x+2y)
As the area of the floor without fountain-pool area is 21 square meter, it gives x2y2=21.
Thus, the system of equations becomes {x+y=20xy=96
Step 3: Modify the equation 4x+2y=24 as y=244x2
Substitute y=244x2 in the equation x2y2=21 and obtain the quadratic equation as,
x2(244x2)2=21
x2576192x+16x24=21
4x2576+192x16x2=84
12x2+192x660=0
That further becomes x216x+55=0.
Solve the equation x216x+55=0 and obtain the value of x as follows.
x216x+55=0
x211x5x+55=0
x(x11)5(x11)=0
(x11)(x5)=0
On further simplification,
x11=0 or x5=0
x=11 or x=5
Substitute x=11 in the equation 4x+2y=24 and obtain the value of y as follows.
4x+2y=24
4(11)+2y=24
44+2y=24
2y=20
y=10
Substitute x=5 in the equation 4x+2y=24 and obtain the value of y as follows.
4x+2y=24
4(5)+2y=24
20+2y=24
2y=4
y=2
Thus, for x=11,y=10, and for x=5,y=2.
The length cannot be negative. Therefore, the solution is (5,2)
Step 4: Check the result, by substituting the obtained solutions in the given original equations

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