Respuesta :
Answer:
The length of the given rectangular patio: L = 28 feet
Step-by-step explanation:
Rectangle is a two-dimensional shape having 4 sides and 4 vertices. It has equal angles and equal alternate sides. Also all the sides of a rectangle are perpendicular to each other.
If a given rectangle has width (W) and length (L), then
The perimeter of the rectangle = 2W + 2L = 2[W + L]
Given: For the rectangular patio, W = 2L - 40.75 feet
Perimeter of rectangular patio = 86.5 feet
L = ? feet
As, Perimeter = 2[W + L]
⇒ 86.5 feet = 2 [(2L - 40.75 feet) + L] = 2 [(3L - 40.75 feet]
⇒ 86.5 feet = 6L - 81.5 feet
⇒ 6L = 86.5 + 81.5 = 168 feet
⇒ L = 168 ÷ 6 = 28 feet
∴ The length of the given rectangular patio: L = 28 feet
The length of the patio for the considered rectangular patio is evaluated to be of 28 feet
What is perimeter?
Its the sum of length of the sides used to made the given figure.
For a rectangle, two of its side are lengths and two of its side are width, therefore,
Perimeter of a rectangle = [tex]2\times length + 2 \times width = 2(L + W) \: \rm units[/tex]
(sign of multiplication is often hidden if there are non numeric symbols and numbers being multiplied are written together)
For this case, we're provided the facts as:
- The patio is rectangular.
- The width of the patio is 40.74 ft shorter than twice its length
- The perimeter of patio is 86.5
Let we suppose that the length of this patio be L feet long
and let we take its width be of W feet long.
Then, we get, from the second fact:
[tex]W = 2L - 40.75[/tex]
And, from the third fact, we get:
[tex]P = 2(L + W)\\86.5 = 2(L + W)[/tex]
Putting the value of W in terms of L in the last equation we obtained, we get:
[tex]86.5 = 2(L + (2L - 40.75)) = 2(3L -40.75) \\86.5 = 6L -81.5\\\\\text{Adding 81.5 on both the sides}\\\\86.5 + 81.5= 6L\\168 = 6L\\\\\text{Dividing both the sides by 6}\\\\\dfrac{168}{6} = \dfrac{6L}{6}\\28 = L\\\\L = 28 \: \rm ft[/tex]
Using this value of L in the equation for W, we get:
[tex]W = 2L - 40.75\\W = 2\times 28 - 40.75 = 56-40.75\\W = 15.25 \: \rm ft[/tex]
Thus, the length of the patio for the considered rectangular patio is evaluated to be of 28 feet
Learn more about perimeter here:
https://brainly.com/question/10466285
