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!!