The area of some shape varies directly with the square of its side. If a shape with 2cm sides has an area 10cm^2,what would be the area of a shape ofthe same type with side of 3cm.
area=k*s^2
10=k*2^2 or k= 2.5
area= 2.5*3^2=2.5*9= you do it.
thank you, i think i got it now.
To find the area of a shape with a 3cm side, given that the area varies directly with the square of the side, we can use the concept of direct variation.
Let's first understand what direct variation means. In a directly proportional relationship, when one quantity increases (or decreases), the other quantity also increases (or decreases) in direct proportion to it. In this case, the area of the shape is directly proportional to the square of its side.
We can set up a proportion to solve this problem. Since area varies directly with the square of the side, we can write:
(2 cm)^2 : 10 cm^2 = (3 cm)^2 : X cm^2
Here, X represents the area of the shape with a 3cm side that we want to find.
Now, let's solve the proportion:
(2 cm)^2 / 10 cm^2 = (3 cm)^2 / X cm^2
4 cm^2 / 10 cm^2 = 9 cm^2 / X cm^2
Simplifying, we get:
2/5 = 9/X
To solve for X, we can cross multiply:
2X = 5 * 9
2X = 45
Dividing both sides by 2:
X = 45 / 2
X = 22.5 cm^2
Therefore, the area of a shape with a 3cm side would be 22.5 cm^2.