The length of a room is 4 times longer than it's width.its area is 36m2.Find the dimensions of the room .
width --- x
length --- 4x
area = x(4x) = 36
4x^2 = 36
x^2 = 9
x = 3
the room is 3 m by 12 m
Let's assume the width of the room is "w" meters.
According to the given information, the length of the room is 4 times longer than its width, which means the length is 4w meters.
The area of a rectangle is given by multiplying its length and width, so we have:
Area = Length × Width
36 = (4w) × w
Now we can solve the equation:
36 = 4w^2
Divide both sides of the equation by 4:
9 = w^2
Take the square root of both sides to solve for "w":
√9 = √(w^2)
3 = w
So, the width of the room is 3 meters.
Now we can find the length by multiplying the width by 4:
Length = 4w = 4 × 3 = 12
Therefore, the dimensions of the room are:
Width = 3 meters
Length = 12 meters
To find the dimensions of the room, we can set up two equations based on the given information.
Let's assume the width of the room is "x" meters.
According to the problem, the length of the room is 4 times longer than its width, which means the length is 4x meters.
The area of the room is the product of the length and the width, which is given as 36 square meters.
So, our equations are:
Length (L) = 4x
Width (W) = x
Area (A) = L * W = 36
We can substitute the values from the equations into the area equation:
36 = (4x) * x
Next, let's simplify the equation by multiplying:
36 = 4x^2
To solve for x, divide both sides of the equation by 4:
36/4 = x^2
9 = x^2
Now, take the square root of both sides to solve for x:
√9 = √x^2
3 = x
Therefore, the width of the room is 3 meters.
We can find the length by multiplying the width by 4:
Length = 4 * 3 = 12 meters
So, the dimensions of the room are width = 3 meters and length = 12 meters.