Answer:
Explanation:
Let's use the formula for the perimeter of a rectangle: P = 2L + 2W, where L is the length and W is the width.
We are given that the perimeter is 20 cm, so:
20 = 2L + 2W
Simplifying this equation, we get:
10 = L + W
We are also given that the area of the rectangle is 24 cm, so:
24 = LW
Now we have two equations with two variables, which we can solve using substitution. Solving the first equation for L, we get:
L = 10 - W
Substituting this expression for L into the second equation, we get:
24 = (10 - W)W
Expanding the brackets and rearranging, we get a quadratic equation:
W^2 - 10W + 24 = 0
We can factor this equation as:
(W - 6)(W - 4) = 0
So the possible values for W are 6 cm and 4 cm. To find the corresponding values for L, we can use the equation L = 10 - W:
If W = 6, then L = 4
If W = 4, then L = 6
Therefore, the dimensions of the piece of metal are 4 cm by 6 cm.