Answer:
Explanation:
Let's start by using some formulas to relate the perimeter and area of a figure.
For a square, the perimeter is 4 times the length of one side (P = 4s) and the area is the length of one side squared (A = s^2).
If we let s be the length of one side of the square, then we can write two equations:
P = 4s
A = s^2
We're given that the perimeter is 14, so we can substitute that in for P:
14 = 4s
Solving for s, we get:
s = 3.5
Now we can find the area by substituting s = 3.5 into the formula for area:
A = s^2 = 3.5^2 = 12.25
However, this area doesn't match the given area of 8. So, we need to try a different shape.
Let's try a rectangle. For a rectangle, the perimeter is twice the length plus twice the width (P = 2l + 2w) and the area is the length times the width (A = lw).
We're given that the perimeter is 14, so we can write:
14 = 2l + 2w
Simplifying:
7 = l + w
We want the area to be 8, so we can write:
8 = lw
Substituting 7 - w for l (from the previous equation), we get:
8 = w(7 - w)
Expanding:
8 = 7w - w^2
Rearranging and factoring:
w^2 - 7w + 8 = 0
This factors to:
(w - 1)(w - 8) = 0
So the possible values for w are 1 and 8. If w is 1, then l is 6, which means the perimeter is 14 but the area is only 6. If w is 8, then l is also 6, which means the perimeter is 14 and the area is 8.
Therefore, a rectangle with dimensions 6 by 1 (or 1 by 6) has a perimeter of 14 and an area of 8.