Answer:
Length: 23.38
Width: 3.34
Step-by-step explanation:
First I drew out a diagram so that I could visibly see the problem. [ a rectangle with 7x on one side and x on the other.
So to find the area you multiply length time width and 7x times x is 7x^2. The actual area is given: 78, so you set that equal to 7x^2.
Then you want to divide by 7 to get 11.14. Then you want to take the square root of 11.14 to get 3.338 which rounds to 3.34 {try not to round until the very end]. This gives you the width of the rectangle, so to find the length you would have to multiply x by 7 to get 23.38. When you multiply the length and width (3.34 x 23.38) you get 78.08 which can round to 78.
7x^2 = 78
x^2 = 78/7
x^2= 11.142...
x = sqrt(1.142...)
x = 3.338 --> 3.34 --> width
3.34 x 7 --> 23.38 --> length
3.34 x 23.38 --> 70.8
Answer:
Width = 6 inches
Length = 13 inches
Step-by-step explanation:
The length of a rectangle is seven inches more than its width. Its area is 78 square inches.
Let w be the width of the rectangle
length is w+7
Area of the rectangle is length time width
[tex]area=w(w+7)[/tex]
[tex]78=w(w+7)[/tex]
[tex]78=w^2+7w[/tex]
Subtract 78 from both sides
[tex]0=w^2+7w-78[/tex]
now factor it and solve for w
product is -78 and sum is +7
[tex]0=w^2+7w-78[/tex]
[tex]0=(w+13)(w-6)[/tex]
Set each factor =0 and solve for x
[tex]w+13=0, so w=-13[/tex]
[tex]w-6=0, so w=6[/tex]
width cannot be negative , so the value of w is 6
Width = 6 inches
Length = width +7=13 inches
