Question

A rectangle has 30 sq. meters and a perimeter of 34 meters what are the dimensions of the rectangle

Answer 1

If the area of the rectangle is 30 sq meters, that means length x width = 30.

So how do we find length and width? Well, they give us the perimeter of 34 which is length×2 + width×2. So if we find 2 factors of 30 that add up to 1/2 of 34, we'll find our length and width.

1/2 of 34 is 17

Let's look at the factors of 30...

1×30
2×15
3×10
5×6

We need the factors that add to 17... 15 + 2 = 17

So we know our rectangle has dimensions

Length 15 meters
Width 2 meters

Let's check the answer...
a = length × width
30 = 15×2
30 = 30 check!

perimeter = 2×L + 2×W
34 = 2×15 + 2×2
34 = 30 + 4
34 = 34. Check!!