The length of a rectangle is 4m more than the width. The area of the rectangle is 45 m squared. Find the length and width.
Please help!
is it 5 and 9?
width --- x
length ----x+4
x(x+4) = 45
x^2 + 4x - 45 = 0
(x+9)(x-5) = 0
x = 5 or x = a negative, which is silly
the width is 5 and the length is 9
check:
is 9 greater than 4 by 5 ? yes
is the area = 5x9 = 45 ? yes
thanks
one more question...
the length of a rectangle is 3 times the width. the area is 108 cm squared. find the dimension of the rectangle.
just change your definitions ...
width --- x
length --- 3x
x(3x) = 108
3x^2 = 108
x^2 = 36
x = √36 = 6
back-substitute to get with and length
To find the length and width of the rectangle, we can use the given information and solve the problem step by step.
Let's suppose the width of the rectangle is "x" meters.
According to the given information, the length of the rectangle is 4 meters more than the width. So, the length would be "x + 4" meters.
The formula for the area of a rectangle is: Area = Length × Width. We know that the area of the rectangle is 45 square meters.
So, we can use this formula and substitute the values we have:
45 = (x + 4) × x
Now, we can solve this equation to find the value of "x" (the width of the rectangle).
Expanding the equation, we get:
45 = x^2 + 4x
Rearranging the equation to make it a quadratic equation:
x^2 + 4x - 45 = 0
Now, we can solve this quadratic equation for "x" using factoring, completing the square, or the quadratic formula.
Factoring the quadratic equation, we find:
(x + 9)(x - 5) = 0
Setting each factor equal to zero:
x + 9 = 0 or x - 5 = 0
Solving each equation for "x", we get:
x = -9 or x = 5
Since the width cannot be negative, we discard x = -9.
Therefore, the width of the rectangle is x = 5 meters.
Now, we can find the length by adding 4 to the width:
Length = Width + 4 = 5 + 4 = 9 meters.
Hence, the length of the rectangle is 9 meters, and the width is 5 meters.