The base of rectangle is 3cm more than twice the height the perimeter is 60cm find the base and height of the rectangle
P = 2L + 2W
60 = 2(2W + 3) + 2W
60 = 4W + 6 + 2W
54 = 6W
9 = W
Why did the rectangle go to the gym? To work on its perimeter! Let's solve this riddle together.
Let's say the height of the rectangle is "x" cm. According to the information given, the base is 3cm more than twice the height, giving us a base of (2x + 3) cm.
The formula for the perimeter of a rectangle is 2(Length + Width). In this case, the length is the base, and the width is the height.
So, the perimeter is 2((2x + 3) + x) = 60 cm.
Let's simplify the equation:
2(3x + 3) = 60.
Now, let's solve for x:
6x + 6 = 60.
6x = 54.
x = 9.
Substituting back into the equations, the base is 2(9) + 3 = 21 cm, and the height is 9 cm.
So, the base of the rectangle is 21 cm, and the height is 9 cm.
Let's solve this step by step:
Step 1: Let's assume the height of the rectangle is "h" cm.
Step 2: According to the given information, the base is 3 cm more than twice the height. So, the base would be (2h + 3) cm.
Step 3: The formula for the perimeter of a rectangle is: Perimeter = 2*(Length + Width).
Step 4: Substitute the values of base and height into the perimeter formula:
60 = 2*((2h + 3) + h)
Step 5: Simplify the equation:
60 = 2*(3h + 3)
60 = 6h + 6
Step 6: Subtract 6 from both sides of the equation:
60 - 6 = 6h
54 = 6h
Step 7: Divide both sides of the equation by 6:
h = 54/6
h = 9
Step 8: Substitute the value of height into the equation for the base:
base = 2h + 3
base = 2(9) + 3
base = 18 + 3
base = 21
So, the height of the rectangle is 9 cm and the base is 21 cm.
To find the base and height of the rectangle, we can start by setting up equations based on the given information.
Let's assume the height of the rectangle is 'h' cm.
The base of the rectangle is given as 3 cm more than twice the height, which means the base can be represented as (2h + 3) cm.
We are also given that the perimeter of the rectangle is 60 cm.
The formula for the perimeter of a rectangle is P = 2(b + h), where P represents the perimeter, b represents the base, and h represents the height.
Substituting the given values, we have:
60 = 2((2h + 3) + h)
Simplifying the equation:
60 = 2(2h + 3 + h)
60 = 2(3h + 3)
60 = 6h + 6
60 - 6 = 6h
54 = 6h
h = 9
Now that we have found the value of h, we can substitute it back into the equation to find the base:
b = 2h + 3
b = 2(9) + 3
b = 18 + 3
b = 21
Therefore, the base of the rectangle is 21 cm and the height is 9 cm.