the length of a rectangle is 7 cm more than its width. find the demensions of the rectangle if its perimeter is 50 cm.
L=w+7
permiter=50=2L+2W=2(w+7)+2W=4W+14
4W=36
solve for W, then L
To find the dimensions of the rectangle, we need to set up an equation based on the given information. Let's denote the width of the rectangle as 'x' cm. Since the length is 7 cm more than the width, the length would be 'x + 7' cm.
The formula for the perimeter of a rectangle is given by:
Perimeter = 2(length + width)
Substituting the given values, we can write the equation as:
50 = 2(x + 7 + x)
Now, let's solve this equation to find the value of 'x'.
50 = 2(2x + 7) [Distribute the 2]
50 = 4x + 14 [Combine like terms]
36 = 4x [Subtract 14 from both sides]
9 = x [Divide both sides by 4]
Therefore, the width of the rectangle is 9 cm. Now we can find the length by substituting this value back into our expression for the length:
Length = Width + 7
Length = 9 + 7
Length = 16 cm
So, the dimensions of the rectangle are 9 cm (width) and 16 cm (length).