AreaWhat is the area of the rectangle whose length is 3 times the width and the perimeter is 24.

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

Let the length and width of the rectangle be L and W.

The perimeter = 2L + 2W = 24

and L = 3W

=> 6W + 2W = 24

=> 8W = 24

=> W = 3

L = 9

The area = L*W = 9*3 = 27

tonys538's profile pic

tonys538 | Student, Undergraduate | (Level 1) Valedictorian

Posted on

For a rectangle with sides L and W, the perimeter is 2*(L+W) and the area is W*L.

The area of a rectangle whose length is 3 times the width and the perimeter is 24 is required.

Let the width be W, the length is 3*W. The perimeter is 2*(3*W+W) = 24

4W = 12

W = 3

L = 9

The area of this rectangle is 27 square units.

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll start by writing the area of a rectangle.

A = length*width

But, from enunciation, length = 3width

A = 3width*width

A = 3width^2

We also know, from enunciation, that the perimeter is P= 24.

P = 2length + 2width

P = 2*(3width) + 2width

P = 8 width

24 = 8 width

We'll divide by 8:

width = 24/8

width = 3

length = 3width

length = 9

A = 3*9

A = 27 square units

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