The length of the rectangle 5cm more than twice the width.The perimeter is 70.What is the area?
The length of the rectangle 5cm more than twice the width.
This mean :
L = 5 + 2 W
P = 2 W + 2 L = 2 ( W + L )
70 = 2 ( W + L )
70 = 2 ( W + 5 + 2W )
70 = 2 ( 3 W + 5 ) Divide both sides by 2
70 / 2 = 2 ( 3 W + 5 ) / 2
35 = 3 W + 5 Subtract 5 to both sides
35 - 5 = 3 W + 5 - 5
30 = 3 W Diwide both sides by 3
30 / 3 = 3 W / 3
10 = W
W = 10 cm
L = 5 + 2 W = 5 + 2 * 10 = 5 + 20 = 25 cm
Proof :
P = 2 ( W + L ) = 2 ( 10 + 25 ) = 2 * 35 = 70 cm
To find the area of a rectangle, you need to know the length and width of the rectangle. In this case, we are given that the length is 5 cm more than twice the width. Let's say the width of the rectangle is "w" cm.
According to the given information, the length of the rectangle is 5 cm more than twice the width, so the length can be expressed as (2w + 5) cm.
To find the perimeter of a rectangle, you add the lengths of all four sides. The formula for the perimeter of a rectangle is: P = 2(length + width).
Given that the perimeter is 70 cm, we can set up the equation as:
70 = 2((2w + 5) + w)
Now solve the equation for "w":
70 = 2(3w + 5)
70 = 6w + 10
6w = 60
w = 10
So, the width of the rectangle is 10 cm.
Now, substitute the value of "w" back into the expression for the length:
length = 2w + 5
length = 2(10) + 5
length = 20 + 5
length = 25
Therefore, the length of the rectangle is 25 cm.
Now that we have the length and width of the rectangle, we can calculate the area. The formula for the area of a rectangle is: A = length * width.
Substituting the values:
A = 25 * 10
A = 250 cm²
Therefore, the area of the rectangle is 250 cm².