the length of a rectangle is 2 less than 3 times the width. the perimeter is 20 cm. find the length, width, and area of the rectangle.
i got stuck after L=3W-2 but i'm not sure what to do after.
Use
Perimeter = 2(L+W) = 20
Substitute L (that you calculated) into the equation, and solve for W, hence L.
2(L+W=20
To find the length, width, and area of the rectangle, we can set up a system of equations using the given information.
Let's begin by assigning variables:
Let L represent the length of the rectangle.
Let W represent the width of the rectangle.
According to the problem, we know two things:
1) The length of the rectangle is 2 less than 3 times the width:
L = 3W - 2
2) The perimeter of the rectangle is 20 cm:
Perimeter = 2(L + W) = 20
Now we can substitute the value of L from the first equation into the second equation:
2((3W - 2) + W) = 20
Simplifying:
2(4W - 2) = 20
8W - 4 = 20
8W = 24
W = 3
Now that we have found the value of W, we can substitute it back into the first equation to find L:
L = 3(3) - 2
L = 9 - 2
L = 7
So, the width of the rectangle is 3 cm, and the length is 7 cm.
To find the area of the rectangle, we can use the formula:
Area = Length x Width
Therefore, the area of the rectangle is:
Area = 7 x 3 = 21 square cm.