The length of a rectangular flag is four yards longer than the width. The area f the flag is 140 square yards. Find the length and the width.
The width equals x, and the length equals 4+x. If the area is 140, then we should have gotten that by doing length times height. Set it up as (x)(4+x)=140. Distribute the x and you would get x^2+4x=140. Since its quadratic, it must be equal to zero. So, minus 140 from both sides and get x^2+4x-140=0. Use factoring or quadratic formula to solve for x. You should get 10 and -14, but use 10 since we usually only use the positive answers.
Let's use algebra to solve this problem.
Let's suppose the width of the flag is x yards.
According to the given information, the length of the flag is 4 yards longer than the width. So, the length of the flag is x + 4 yards.
The area of a rectangle is given by the formula: Area = Length * Width.
In this case, the area of the flag is 140 square yards. So, using the above formula, we have:
140 = (x + 4) * x
Now, let's solve this equation step by step.
Expanding the equation:
140 = x^2 + 4x
Rearranging the equation in standard quadratic form:
x^2 + 4x - 140 = 0
Now, let's solve this quadratic equation either by factoring or by using the quadratic formula.
By factoring:
(x + 14)(x - 10) = 0
Setting each factor to zero:
x + 14 = 0 or x - 10 = 0
Solving for x in each equation:
x = -14 or x = 10
Since the width cannot be negative, the only valid solution is x = 10.
Therefore, the width of the flag is 10 yards.
Now, we can find the length by adding 4 to the width:
length = width + 4 = 10 + 4 = 14 yards.
So, the length and width of the flag are 14 yards and 10 yards, respectively.
To find the length and width of the rectangular flag, we can set up a system of equations based on the given information.
Let's assume:
- Width of the flag = W yards
- Length of the flag = L yards
According to the given information, we have two conditions:
1. Length is four yards longer than the width, so L = W + 4.
2. The area of the flag is 140 square yards, so L * W = 140.
Using these two conditions, we can solve the system of equations.
Substituting L in terms of W from the first equation into the second equation:
(W + 4) * W = 140.
Expanding the equation:
W^2 + 4W = 140.
Rearranging the equation into standard quadratic form:
W^2 + 4W - 140 = 0.
Now, we can solve this quadratic equation.
Factoring the quadratic:
(W - 10)(W + 14) = 0.
Setting each factor to zero:
W - 10 = 0, which gives W = 10.
W + 14 = 0, which gives W = -14.
Since we are dealing with measurements, a negative value for the width does not make sense in this context. So, we ignore W = -14.
Therefore, the width of the flag is W = 10 yards.
Substituting the value of W into the equation L = W + 4:
L = 10 + 4 = 14.
Hence, the length of the flag is L = 14 yards, and the width is W = 10 yards.