xavierbrotherton
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the area of a rectangular patio is 105 ft2. The length of the patio is 8 ft longer than the width of the patio. This can be represented by the equation w2 + 8w - 105 = 0. What is the width of the patio in feet?

Sagot :

reinhard10158

Answer:

7 ft

Step-by-step explanation:

the area of a rectangle is

length × width

in our case

length × width = 105 ft²

and we know

length = width + 8

that identity we can use in the area equation and get

(width + 8) × width = 105

width² + 8width = 105

width² + 8width - 105 = 0

and that is how your teacher got the equation

w² + 8w - 105 = 0

the general solution for such a quadratic equation is

w = (-b ± sqrt(b² - 4ac))/(2a)

with our equation

a = 1

b = 8

c = -105

w = (-8 ± sqrt(8² - 4×1×-105))/(2×1) =

= (-8 ± sqrt(64 + 420))/2 = (-8 ± sqrt(484))/2 =

= (-8 ± 22)/2 = -4 ± 11

w1 = -4 + 11 = 7

w2 = -4 - 11 = -15

negative values/ solutions for side lengths of shapes don't make sense, so the only valid solution is w = 7 ft

Lanuel

The width of the rectangular patio in feet is equal to -15 or 7 feet.

  • Let the length of the rectangle be L.
  • Let the width of the rectangle be W.

Given the following data:

  • Area of a rectangular patio = 105 [tex]ft^2[/tex].
  • [tex]L=W+8[/tex]

How to calculate the area of a rectangle.

Mathematically, the area of a rectangle is given by the formula;

[tex]A=LW[/tex]

Substituting the given parameters into the formula, we have;

[tex]W^2 +8W-105=0\\\\W^2 +15W-7W-105=0\\\\W(W+15)-7(W+15)=0\\\\(W+15)(W-7)=0[/tex]

Width, W = -15 or 7 feet.

Read more on area of a rectangle here: https://brainly.com/question/25292087

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