Answer:
Length = 9 m
Width = 6 m
Explanation:
The formula for the area of a rectangle is given by:
A = lw, where
- A is the area in units squared,
- l is the length,
- and w is the width.
Step 1: Create an equation to model the width being 3 m less than the length:
- Since we're told that the width is 3 m less than the length, we can model this with the following equation:
w = l - 3
Step 2: Substitute 54 for A and l - 3 for w in A = lw
Now we can plug in 54 for A and l - 3 for w in A = lw:
54 = l(l - 3)
54 = l^2 - 3l
0 = l^2 - 3l - 54
Step 3: Factor l^2 - 3l - 54 to solve the quadratic:
- We can solve the quadratic using factoring.
- Remember that when a variable is by itself, you can think of an imaginary 1 being in front of it.
- Thus, l^2 is the same as saying 1 * l^2.
- Nevertheless, we wan to find two numbers whose product is equivalent to 1 * -54 and whose sum is -3.
- We know that 6 * -9 = -54 and 6 + (-9) = -3. Thus, our two factors are 6 and -9.
(l + 6)(l - 9) = 0
Step 4: Set both terms equal to 0 to solve for l:
Setting (l + 6) equal to 0:
l + 6 = 0
l = -6
Setting (l - 9) equal to 0:
l - 9 = 0
l = 9
Because we can't have a negative measure, l is 9 m.
Step 5: Plug in 9 for l in w = l - 3 to find w, the width:
w = 9 - 3
w = 6
Thus, the length is 9 m and the width is 6 m.