Question

The length of a rectangle is 4.2 cm more than 2 times the width. If the perimeter of the rectangle is 42.6 cm, what are its dimensions?

2 points for showing the steps

1 point for correctly finding the width and length each

Answer 1

Hi there!

The general formula to find the perimeter of a rectangle is :

P = (Length × 2) + (Width × 2)

Let's say the width of the rectangle is "x".

The lenght of the rectangle is equal to 2x + 4.2

Replace everything you know in the formula :

42.6 = ((2x + 4.2) × 2) + ((x) × 2)

Simplify everything :

2x × 2 = 4x

4.2 × 2 = 8.4

x × 2 = 2x

42.6 = 4x + 8.4 + 2x

42.6 = 6x + 8.4

Isolate "x":

42.6 = 6x + 8.4

Subtract 8.4 from each side of the equation

34.2 = 6x

Divide each side of the equation by 6

5.7 = x

5.7cm = the width of the rectangle

Since the lenght of the rectangle is equal to 2 times the width of the rectangle plus 4.2 :

Length = (2 × 5.7) + 4.2

Length = 15.6cm

42.6 = (2 × 15.6) + (2 × 5.7) ? → YES

There you go! I really hope this helped, if there's anything just let me know! :)