The area of a rectangular barn is 140 square feet. it's length is 4 feet longer than the width. find the length and width of the wall of the barn

Width = 10 feet; Length = 14 feet

Step-by-step explanation:

Let the width = w. The length is 4 feet longer so the length = w + 4.

Area = length x width.

w(w + 4) = 140

Distribute

w^2 + 4w = 140

Set up as quadratic

w^2 + 4w - 140 = 0

Factor

(w + 14)(w - 10)

Set equal to zero and find w.

w + 14 = 0, so w = -14

w - 10 = 0, so w = 10

You cannot have a negative width, so -14 is out. The width is 10 feet.

Length = w + 4; (10) + 4 = 14 feet.

step-by-step explanation: so we look at the formula un = a + (n-1)d

un is the amount of seats

n is the nth term aka row number

a is the original sequence/row number

d is the difference between each term

so in this a=22 d=6 and n can remain as n because we are simply formjng a rule

lets put these in the equation

un=22+(n-1)(6)

this is your answer to part a

however

lets double check that this is correct, we'll try putting it into the second term

un=a+(n-1)d

u2=22+(2-1)(6)

u2=22+6

u2=28

as the question said the second row has 28 seats so now we know the formula we made is correct.

as for part b

un=a+(n-1)

its asking us to find a row with 100 seats.

remember un was the amount of seata so all we do is substitute this in.

un=100 a=22 d=6

un=a+(n-1)d

100=22+(n-1)(6)

so now we simplify to find n which is the row number.

100-22=22+(n-1)(6)-22

78=(n-1)(6)

78/6=(n-1)(6)/6

13=n-1

13+1=n-1+1

14=n

so now we know that in the 14th row there is 100 seats.

hope this and that you understood! its my first time using the app or anyone out on here : p its also me to revise so a bunch! ask more questions if you dont understand ☺