contestada

You plant a rectangular rose garden along the side of your garage. you enclose 3 sides of the garden with 40 feet of fencing. the total area of the garden is 100 square feet. find the possible dimensions of the garden. round to the nearest tenth.

Respuesta :

taskmasters
let x be the length of the garden
and y be the width of the garden.

since you only enclose 3 sides of the garden by a 40 ft fence. so the equation for this is:

2x + y = 40

and the area of the garden is 100 sq ft, so in equation
xy = 100
from equation 1, 2x + y = 40
y = 40 - 2x
substitute to equation 2

xy = 100
x ( 40 - 2x) = 100
40x - 2x^2 = 100
2x^2 - 40x + 100 = 0

x = 2.9 ft
y = 34.5 ft 

The dimensions of the rectangular rose garden along the side of the garage is 17.1 and 2.9 feet to the nearest tenth.

What is the area of a rectangle?

Area of a rectangle is the product of the length of the rectangle and the width of the rectangle. It can be given as,

A=a\times b

Here, (a)is the length of the rectangle and (b) is the width of the rectangle

The rose garden is in the shape of the rectangular. Suppose the one side of the garden is a meters long and another side of the garden is b meters long.

As, the three, 3 sides of the garden has 40 feet of fencing. Thus,

[tex]a+b+a=40\\2a+b=40\\b=40-2a[/tex]     ......1

Let the above equation is equation 1.

The total area of the garden is 100 square feet. Therefore,

[tex]ab=100\\b=\dfrac{100}{a}[/tex]

Put this value in the equation 1 as,

[tex]\dfrac{100}{a}=40-2a\\100=40a-2a^2\\2a^2-40a+100=0[/tex]

On solving this quadratic equation, we  get the value of x as, 17.07 and 2.92.

Therefore, the dimensions of the rectangular rose garden along the side of the garage is 17.1 and 2.9 feet to the nearest tenth.

Learn more about the area of rectangle here;

https://brainly.com/question/11202023

Otras preguntas