PsychoPunch
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SIXTY POINTS
Jose needs to enclose a rectangular section of his yard. The perimeter of the section is 27 feet, and the area is 35 square feet. Find the length and width of the section.
Part I: Let L = length of the section and let W = width of the section. The equation for the perimeter is P = 2(L + W). If the perimeter is 27 feet, solve for W. Show your work. (1 point)

Part II: The equation for area is A = LW. Substitute the expression you found for W in Part I into the area equation. Then, if the area is equal to 35 square feet, write the equation in standard form with a, b, and c as whole numbers. (3 points)

Part III: Use the quadratic formula, , to solve for L. Show your work. (2 points)

Part IV: Use the solution for L in Part III to find the corresponding values for W. Show your work. When you're done, state the dimensions of the section. 

Respuesta :

Let the width be W and length be L 

LW = 35 

L = 35/W 

Perimeter = 2 ( Length + Width ) 

27 = 2 ( 35/W + W ) 

13.5 = (35+ W^2) / W 

W^2 - 13.5W + 35 = 0 

W^2 - 10W - 3.5W +35 = 0 

W ( W -10) - 3.5 ( W - 10) = 0 

( W-3.5) ( W-10) = 0 

W = 3.5 or 10 

ANSWER Width = 3.5' Length = 10'
MrRoyal

The dimension of the section is 3.5 by 10 feet

Part I : Solve for W

The equation is given as;

P = 2(L + W).

Substitute 27 for P

2(L + W) = 27

Divide through by 2

L + W = 13.5

Subtract L from both sides

W = 13.5 - L

Part II: Write the equation of area

We have:

A = LW

Substitute W = 13.5 - L

A = (13.5 - L) * L

Expand

A = 13.5L - L^2

A = 35.

So, we have:

13.5L - L^2 = 35

Multiply through by 2

27L - 2L^2 = 70

Rewrite as:

2L^2 - 27L + 70 = 0

Part III: Solve for L using quadratic formula

We have:

2L^2 - 27L + 70 = 0

This means that:

a = 2, b = -27 and c = 70

The quadratic formula is:

[tex]L = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}}[/tex]

So, we have:

[tex]L = \frac{27 \pm \sqrt{(-27)^2 - 4*2*70}}{2*2}}[/tex]

Evaluate

[tex]L = \frac{27 \pm 13}{4}}[/tex]

Split

L = (27 + 13)/4 and (27 - 13)/4

Solve

L = 10 and 3.5

Part IV: Calculate W

We have:

W = 13.5 - L

This means that:

W = 13.5 - 10 and W = 13.5 - 3.5

Evaluate

W = 3.5 and 10

Hence, the dimension of the section is 3.5 by 10 feet

Read more about area and perimeter at:

https://brainly.com/question/24571594

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