the length of a rectangle is 4 times of its width.the perimeter of the rectangle is 150cm. find the linear equations?
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let length=l=x
and width=w=y
as given length is 4 times of its width so, x= 4y
as perimeter of rectangle is equal to 2(length+width)
so,according to given condition
2(x+y)=150
2x+2y=150
To find the linear equations, we need to understand the relationship between the length and width of the rectangle.
Let's denote the width of the rectangle as 'w' and the length as 'l'. According to the information given, the length of the rectangle is 4 times its width.
Therefore, we can write the equation as:
l = 4w
Now, we are also given the perimeter of the rectangle, which is 150cm. The perimeter is the sum of all four sides of the rectangle.
The formula for the perimeter of a rectangle is:
Perimeter = 2l + 2w
Substituting the value of 'l' from our earlier equation, we get:
150 = 2(4w) + 2w
Simplifying, we can rewrite the equation as:
150 = 8w + 2w
Combining like terms, we have:
150 = 10w
Dividing both sides of the equation by 10, we find:
w = 15
Now that we know the value of 'w', we can substitute it back into our original equation to find 'l':
l = 4w
l = 4(15)
l = 60
So, the width of the rectangle is 15cm and the length is 60cm.
The linear equations that represent the relationship between the length and width of the rectangle are:
l = 4w
and
w = 15