find the length and width

Question

In a smal rectangular wallet photo the width is 4 cm less than the length. If the border (perimeter) of the photo is 20 cm, find the length and width.

Answer 1

Ramona, Algebra makes this sort of question easy, that's what it's for, but perhaps you haven't done algebra yet. A non-algebraic way is this: You ought to remember always that two sides of every rectangle (the length and the width) are always equal to half the perimeter, so in this case together they would be 10cm. So the two sides must add to 10. We can do this by elimination. It can't be 10, because then it would be just a line, so we start with nine and subtract 4cm = 5cm, now 5+9 is way more than 10, you don't even have to work it out. Then 8-4 = 4, and 4+8 is still more than 10. So try 7-4 =3, and 3+7 = 10. Bingo!

 

 

Answer 2

Alright, Ramona, the first thing you should do is draw a rectangle and label the sides.

 

Let's let x = the length of the rectangle.  Then the width is x-4, right?  Label your rectangle.

 

Now, how do we find the perimeter of a rectangle?  The sum of all your sides should equal 20.  Can you come up with the equation?  Now combine like terms and solve for x.

 

Hope this helps!