The area of this rectangle is 10cm2, find the value of x and use it to find the length and the width of the rectangle. If the length of a rectangle is three time the width and it’s perimeter is 24 cm, what is its area?

Length and width of the rectangle are 4 cm and 2.5 cm respectively.

Given in the picture,

        (4x + 2) cm and (10x - 1) cm

By the property of a rectangle, measure of opposite sides of a rectangle are always equal,

(4x + 2) = (10x - 1)

(4x + 2) - 4x = (10x - 1) - 4x

2 = 6x - 1

2 + 1 = (6x - 1) + 1

3 = 6x

Now we can get the length of the given rectangle by substituting the value of 'x' in (10x - 1) or (4x + 2).

(10x - 1) =

            = 4 cm

Since, area of a rectangle is given by the expression,

Area = Length × width

By substituting the values in the expression,

10 = 4 × width

Width =

           = 2.5 cm

        Therefore, length and width of the rectangle are 4 cm and 2.5 cm respectively.

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