The length of a rectangle is 8 cm greater than its width. Find the dimensions of the rectangle if its area is 105 cm.
How do I solve?
Area = Length*Width
Information you are given:
Area = 105cm^2
and
Length = width + 8
therefore:
105 = (width + 8)*width
105 = width^2 + 8*width
105 = w^2 + 8w
rearranging we get a quadratic:
w^2 + 8w - 105 = 0
w^2 - 7w +15w - 105 = 0
w(w - 7) + 15(w - 7) = 0
(w - 7)(w + 15) = 0
The two possible solutions are
width = 7 or width = -15
Well, the width must be a positive measurement so we take the width = 7
So the answer is:
Width = 7
Length = 7 + 8 = 15
Ok,
Hope that helps
The width of a rectangle is 34 units less than its length period if x is the rectangle's length, then it's area is?
To solve this problem, we can start by setting up an equation based on the given information.
Let's assume the width of the rectangle is x cm. Since the length is 8 cm greater than the width, the length will be (x + 8) cm.
The area of a rectangle is calculated by multiplying its length by its width. According to the problem, the area is 105 cm².
So, we can write the equation as:
Length × Width = Area
(x + 8) cm × x cm = 105 cm²
To simplify the equation, we can multiply the terms:
x(x + 8) = 105
Now let's solve this quadratic equation for x by expanding and simplifying:
x² + 8x = 105
Rearrange the equation in standard quadratic form:
x² + 8x - 105 = 0
Now, we can either factor this quadratic equation or use the quadratic formula to find the value of x. Let's use factoring in this case.
The factors of -105 that add up to 8 are 15 and -7.
So the factored form of the equation can be written as:
(x + 15)(x - 7) = 0
Setting each factor equal to zero and solving for x, we get:
x + 15 = 0 or x - 7 = 0
Solving each equation individually:
x = -15 or x = 7
Since the dimensions of a rectangle cannot be negative, we ignore the negative value.
Therefore, the width of the rectangle is x = 7 cm.
To find the length, we can substitute the value of x into the expression for the length:
Length = x + 8 = 7 cm + 8 cm = 15 cm
So, the dimensions of the rectangle are:
Width = 7 cm
Length = 15 cm.
To solve this problem, we need to use the given information to set up an equation and solve it.
Let's assume the width of the rectangle is 'w' cm. According to the problem, the length is 8 cm greater than the width, so the length can be written as 'w + 8' cm.
The formula for the area of a rectangle is given by:
Area = Length * Width
In this case, the area is given as 105 cm, so we can write the equation as:
105 = (w + 8) * w
To solve this equation, we can start by simplifying it and bringing it to the standard quadratic form.
105 = w^2 + 8w
Rearranging the equation to bring all terms to one side, we have:
w^2 + 8w - 105 = 0
Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula.
Let's factor the quadratic equation:
(w - 7)(w + 15) = 0
Setting each factor equal to zero and solving for 'w', we have two possible solutions:
w - 7 = 0 => w = 7
w + 15 = 0 => w = -15 (discard this solution as width can't be negative)
Therefore, the width of the rectangle is 7 cm.
Now, we can substitute this value back into the equation for the length:
Length = width + 8 = 7 + 8 = 15 cm
So, the dimensions of the rectangle are 7 cm (width) and 15 cm (length).