the length of a rectangle is 5m more than twice its width. and the area of the rectangle is 88m^2. find the dimensions of the rectangle.
Let
w=width, then
length = 2w+5 m
Area = 88 m²
w(2w+5)=88
2w²+5w-88=0 ...(1)
Solve for w in equation (1) by factorization or otherwise and reject the negative root.
a=198 in. ^2
x+7
what is the length and width ?
To find the dimensions of the rectangle, we can use the given information to form two equations. Let's denote the width of the rectangle as 'w' and the length as 'l'.
According to the problem, the length of the rectangle is 5m more than twice its width. This can be written as:
l = 2w + 5 (Equation 1)
The problem also states that the area of the rectangle is 88m². The formula for calculating the area of a rectangle is:
Area = Length × Width
Substituting the values from Equation 1, we get:
w × (2w + 5) = 88
Now, we can solve this equation to find the dimensions of the rectangle.
Step 1: Expand the equation
2w² + 5w = 88
Step 2: Rearrange the equation to the standard quadratic form
2w² + 5w - 88 = 0
Step 3: Solve the quadratic equation
There are multiple methods to solve a quadratic equation, such as factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula:
The quadratic formula is given by:
w = (-b ± √(b² - 4ac)) / (2a)
For our equation: 2w² + 5w - 88 = 0, we have:
a = 2, b = 5, c = -88
Substituting these values in the quadratic formula, we get:
w = (-5 ± √(5² - 4×2×(-88))) / (2×2)
Step 4: Simplify the equation
w = (-5 ± √(25 + 704)) / 4
w = (-5 ± √729) / 4
w = (-5 ± 27) / 4
w = (22 / 4) or w = (-32 / 4)
w = 5.5 or w = -8
Since the width of a rectangle cannot be negative, we discard the value of w = -8.
Therefore, the width of the rectangle is w = 5.5m.
Step 5: Calculate the length of the rectangle
Using Equation 1, substitute the value of w:
l = 2w + 5
l = 2(5.5) + 5
l = 11 + 5
l = 16
Therefore, the length of the rectangle is l = 16m.
In conclusion, the dimensions of the rectangle are:
Width = 5.5m
Length = 16m