The length of a rectangle is 2 centímeters more than three times the width. The area of the rectangle is 120 cm square. Find the dimensions of the rectangle.

Question

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Answer 1

We are told length, L, is 2cm more than 3 times width, W:

L = 2cm + 3W,

and area, A, is 120 cm²:

A = 120 cm².

Recall that the area of a rectangle is:

A = LW,

so if we substitute for A and L, you will have a quadratic equation for W:

120cm² = (2cm + 3W)W.

The dimensions imply that solving for W will give us a value with units of centimeters, so we can now drop cm units:

120 = (2 + 3W)W

3W² + 2W - 120 = 0

Using the quadratic equation formula gives two answers. We only care about the positive answer because W represents width (negative answers make no sense).

We find W = 6cm, and use the equation for L to find:

L = (2cm + 3(6cm)) = 20 cm.

Thus the dimensions of the rectangle are W = 6cm and L = 20cm.