The width of a rectangle is two-thirds its length. If the perimeter is 180 meters, find the dimensions of the rectangle and choose the option which follows.

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Length is 36m and width is 54m.

Length is 54m and width is 36m.

Length is 45m and width is 63m.

Length is 63m and width is 45m.

answer is A.

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Detailed Solution

It is given a rectangle whose width is two-third of its length and the perimeter of the rectangle is 180m.
So, let us assume that the length of the rectangle is x. Then, according to the question, the width is two-third of the length.
So, the width of the rectangle will be

23 x

.
Now, the formula for the perimeter of the rectangle is given as follows,

P = 2 (l + b)

, where ‘p’ is the perimeter, ‘l’ is the length and ‘b’ is the width of the rectangle.
Substituting the values as per the assumptions and the given condition, we have the equation as follows,

128 = 2 x + 23 x

Now, we will solve this equation for the value of x. So, we will begin with simplifying the left side of the equation using the distributive property of multiplication as follows,

2 (x) + 2 23 x = 180 2 x + 43 x = 180

3 (2 x) + 3 43 x = 3 (180) 6 x + 4 x = 540 10 x = 540

10 x 10 = 54010 x = 54

So, we get the length of the rectangle as 54m. Now, for the width, we will substitute the value of x in the expression for the width as per the assumption as follows,