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

Dilated by a factor of 7 is 196 in²

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