Answer:
The width of the garden is 10 yards.
The length of the garden is 30 yards.
Step-by-step explanation:
Let [tex]x[/tex] be the width of the garden so [tex]x+20[/tex] is its length.
We now that the area of a rectangle is width times length, so the area of our garden is [tex]x(x+20)[/tex]. We also now that the area of the garden is 300 square yards so [tex]x(x+20)=300[/tex]
Now we can solve our equation for [tex]x[/tex] to find the dimensions of our garden
[tex]x(x+20)=300[/tex]
[tex]x^{2} +20x=300[/tex]
[tex]x^{2} +20x-300=0[/tex]
- Splitting the middle term:
[tex]x^{2} +30x-10x-300=0[/tex]
- Grouping similar terms:
[tex](x^{2} -10x)+(30x-300)=0[/tex]
[tex]x(x-10)+30(x-10)=0[/tex]
[tex](x-10)(x+30)=0[/tex]
- Using the zero property:
[tex]x-10=0[/tex] or [tex]x+30=0[/tex]
[tex]x=10[/tex] or [tex]x=-30[/tex]
Since distances cannot be negative, [tex]x=10[/tex] is the solution of our equation (and the width of our garden). Since the length is 20 yards more than the width, the length of our garden is 10 + 20= 30 yards.
The length and width are 30 and 10.
It is a polygon that has four sides and four corners. The sum of the internal angle is 360 degrees. In rectangle opposite sides are parallel and equal and each angle is 90 degrees. And its diagonals are also equal and intersect at mid-point.
Given
The length of the garden is 20 yards greater than its width.
Area of garden = 300.
The length and width of the garden.
Let L be the length and W be the width.
The length of the garden is 20 yards greater than its width.
L = W + 20
Then area will be
[tex]\begin{aligned} \rm Area &= \rm length * width\\300 &= L *W\\300 &= (W+20)* W\\W^{2} +20W - 300 &= 0\\W &= 10, -30\end{aligned}[/tex]
SO W = 10 then length will be
L = W + 20
L = 10 + 20
L = 30
Thus the length and width are 30 and 10.
More about the rectangle link is given below.
https://brainly.com/question/10046743
