The length of a rectangle is 3 cm less than 4 times its width. The perimeter is 74 cm. Find the length
P = 2L + 2W
74 = 2(4W - 3) + 2W
74 = 10W - 6
80 = 10W
8 = W
Thank you Ms. Sue
I get the same answer. The problem is that teacher offer this answers:
a. 29 cm
b. 28 cm
c. 27 cm
d. 33 cm
What did we do wrong?
The length is one of your choices of answers. You know the width is 8. Now find the length of one side.
I needed to know more about the solving of maths different problems of different unit topics
Ah, the mysteries of rectangles and their witty lengths! So, let's solve this puzzling riddle. We know that the length of our rectangle is 3 cm less than 4 times its width. So, let's call the width "W". That means the length is 4W - 3 cm. Now, the formula for the perimeter of a rectangle is P = 2L + 2W, where P is the perimeter, L is the length, and W is the width. In our clownish scenario, the perimeter is 74 cm, so we can set up the equation as follows: 74 = 2(4W - 3) + 2W. Now, let's do some clown-like mathematical acrobatics to solve it. Simplifying the equation, we get: 74 = 8W - 6 + 2W. Combining like terms, we have: 74 = 10W - 6. Adding 6 to both sides, we find: 80 = 10W. Finally, dividing both sides by 10, we discover that W, the width of our rectangle, is 8 cm. So, if we substitute that value in the expression for the length (which is 4W - 3), we get: L = 4(8) - 3, which simplifies to L = 32 - 3. And voila! The length of our rectangle is 29 cm. Ta-da!
To find the length of the rectangle, we can set up the given information as an equation.
Let's assume the width of the rectangle is "W" cm.
According to the problem, the length of the rectangle is 3 cm less than 4 times its width. Therefore, the length can be expressed as "4W - 3" cm.
The formula for the perimeter of a rectangle is given by P = 2L + 2W, where P is the perimeter, L is the length, and W is the width.
Given that the perimeter is 74 cm, we can substitute the values into the formula and set up the equation:
74 = 2(4W - 3) + 2W
Simplifying the equation:
74 = 8W - 6 + 2W
Combining like terms:
74 = 10W - 6
Add 6 to both sides of the equation:
74 + 6 = 10W
80 = 10W
Now, divide both sides of the equation by 10:
80/10 = W
W = 8
Therefore, the width of the rectangle is 8 cm.
To find the length, substitute the value of the width into the equation for the length:
Length = 4W - 3
Length = 4(8) - 3
Length = 32 - 3
Length = 29
Therefore, the length of the rectangle is 29 cm.