The area of a rectangular wall of a bran is 96 square feet. Its length is 4ft. longer than the width. Find the length and width of the wall.
To find the length and width of the wall, we can use algebraic equations based on the given information.
Let's denote the width of the wall as "x" feet.
According to the problem, the length of the wall is 4 feet longer than the width. So, the length can be expressed as "x + 4" feet.
Now, we can use the formula for the area of a rectangle, which is length multiplied by width:
Area = Length * Width
Since we know that the area of the wall is 96 square feet, we can write the equation:
96 = (x + 4) * x
To solve this equation for the width of the wall, we need to multiply out the expression:
96 = x^2 + 4x
Rearranging the equation to bring all terms to one side:
x^2 + 4x - 96 = 0
Now, we can solve this quadratic equation by factoring or using the quadratic formula. Factoring is quicker in this case:
We need to find two numbers whose sum is 4 and whose product is -96. By trial and error, we can determine that the numbers are 8 and -12.
Therefore, the quadratic equation factors into:
(x + 12)(x - 8) = 0
Setting each factor to zero and solving for x:
x + 12 = 0 or x - 8 = 0
x = -12 or x = 8
Since the width of a wall cannot be negative, we can ignore the x = -12 solution. Therefore, the width of the wall is 8 feet.
To find the length, we substitute the width value into the expression for the length:
Length = x + 4 = 8 + 4 = 12 feet
Thus, the width of the wall is 8 feet, and the length is 12 feet.
L(ength) = W(idth) + 4
L * W = 96
Substitute W+4 for L in the second equation to find W. Insert that value into the first equation to find L. Check your answers by inserting both values into the second equation.
I hope this helps. Thanks for asking.