Question

Stanford University's soccer field has an area of 8,800 square yards. Its length is 30 yards longer than its width. Write an equation and solve for the dimensions of the soccer field. Will give brainliest to the best of 2 answers!

Answer 1

Let x = the width and x + 30 = the length.

x(x + 3) = 8800

x^2 + 3x = 8800

x^2 + 3x - 8800 = 0

Using the Quadratic Formula, I get x ≈ 92.320 yd and x + 30 ≈ 122.320 yd.

2x + 2x + 60 = 600

4x + 60 = 600

4x = 540

x = 135

x + 30 = 165

The area would be 22275 yd^2.

Answer 2

Answer:

110 yards and 80yards

Step-by-step explanation:

Given: Stanford University's soccer field has an area of $8800$ square yards. Its length is $30$ yards longer than its width.

To Find: Write an equation and solve for the dimensions of the soccer field.

Solution:

Total area of Stanford University's soccer field$=8800$ $\text{square yards}$

let the length of soccer field is$=\text{l}$

let the width of soccer field is$=\text{b}$

Now,

as given

$\text{l}=\text{b}+30$

We know that

area of soccer field$=\text{length}\times\text{width}$

putting values

$\text{l}\times\text{b}$$=8800$

$\text{b}(30+\text{b})=8800$

equation for width of  soccer field

$\text{b}^{2}+30\text{b}-8800=0$

$(\text{b+110})(\text{b}-80)=0$

as $\text{b}$ can not be negative

$\text{b}=80$ $\text{yards}$

$\text{l}=\text{b}+30$

$\text{l}=110$ $\text{yards}$

the dimensions of soccer field are $110$ $\text{yards}$ and $80$ $\text{yards}$