The width of a rectangle ia two third of its length and the length exceeds the width by 7 cm. Find the perimeter of the rectangle
length ---- x
width = 2x/3
x - 2x/3 = 7
once you have the width and length,
perimeter = 2widths + 2lengths
To find the perimeter of a rectangle, we need to know its length and width.
Let's assume the length of the rectangle is "L" cm and the width of the rectangle is "W" cm.
From the given information, we can deduce two equations:
1. The width is two-thirds of the length: W = (2/3) * L
2. The length exceeds the width by 7 cm: L = W + 7
Now we can solve these equations to find the values of L and W.
Substituting the value of L from the second equation into the first equation, we get:
W = (2/3) * (W + 7)
Multiplying both sides of the equation by 3 to eliminate the fraction, we get:
3W = 2(W + 7)
Expanding the equation, we have:
3W = 2W + 14
Subtracting 2W from both sides of the equation, we get:
W = 14
Now we can substitute this value of W back into the second equation to find L:
L = W + 7 = 14 + 7 = 21
So, the width of the rectangle is 14 cm and the length is 21 cm.
To find the perimeter, we use the formula: Perimeter = 2 * (Length + Width)
Substituting the values, we get:
Perimeter = 2 * (21 + 14) = 2 * 35 = 70 cm
Therefore, the perimeter of the rectangle is 70 cm.