Question

The width of a rectangle is three fourths of the length. The perimeter of the rectangle becomes 50 cm when the length and the width are each increased by 2 cm. Find the length and the width.

Answer 1

First of all look at the equation for perimeter. (Let's use n for length, and w for width)

P=2n+2w

Next, since the width is 3/4 the length (n) replace w with that information.

P=2n+2(3/4)n
Now we only have one variable in our equation.

Let's take care of the P value. The perimeter equals 50cm, but only when the length and the width have 2 more cm added to them. So we can use this information to finish writing the equation.

Replace P with 50, and add 2 to the length and width. (Remember length =2n, and width = 2(3/4)n = (6/4)n =3n/2 Notice that I kept the n outside of the parenthesis to emphasize that n is in the numerator.)

50=(2n+2)+(3n/2+2) Solve for n.

Answer 2

Now I solved and got 92/7 which may be wrong, but hopefully this will give you an idea on how to solve this. Anyway, now that you have the length, you can multiply by 3/4 to get the width.