Question

A square with an area of 4 in² is dilated by a factor of 7. What is the area of the dilated square?

Answer 1

Dilated by a factor of 7 is 196 in²

Answer 2

Area of square if the square is s inches long is 4 in²
s² = a
s² = 4

When a square is dilated by a factor of 7, the length of side is also dilated by the factor of 7. For an instance, s₁ represents the dilated side. The equation will be
s₁ = 7s

Find the new area, the new area is represented by a₁
a₁ = s₁²
Because s₁ is equal to 7s, substitute s₁ with 7s
a₁ = (7s)²
a₁ = 7² s²
a₁ = 49s²
The value of s² is 4, substitute s² with 4
a₁ = 49(4)
a₁ = 196
The new area is 196 in²