Answer:
W = 8cm
L = 19cm
Explanation:
The first step to solving these problems is always writing the information that is given into 2 equations.
Piece of info #1: Length is 5cm less than 3 times the width
Piece of info #2: Perimeter (of the rectangle, which has 4 sides) is 54cm
Turing these into equations...
Equation 1) L = 3*W - 5
Equation 2a) L+L+W+W = 54
Let's simplify that second equation:
Equation 2b) 2L+2W = 54
Now, we just solve the system of two equations by substitution. Take the known value of L from equation 1 and substitute it in for the value of L in equation 2b:
2*(3*W-5)+2W = 54
Now we solve for W:
6W - 10 + 2W = 54
8W - 10 = 54
8W = 64
W = 64/8
W = 8 cm
Now that we know W, we can substitute its value into either equation 1 or equation 2 to find L. Here, I'll randomly choose equation 1.
Equation 1) L = 3*W - 5
L = 3*8 - 5
L = 24-5
L = 19 cm