32-162k^2=0

solve the equation by factoring. check solutions.

see explanation

Step-by-step explanation:

given 32 - 162k² = 0 ( factor out 2 from each term )

2(16 - 81k²) = 0

16 - 81k² ← is a difference of squares and factors in general as

• a² - b² = (a - b)(a + b)

16 = 4² ⇒ a = 4

81k² =(9k)² ⇒ b = 9k

16 - 81k² = (4 - 9k)(4 + 9k), thus

32 - 162k² = 0

2(4 - 9k)(4 + 9k) = 0

Equate each factor to zero and solve for k

4 - 9k = 0 ⇒ k =

4 + 9k = 0 ⇒ k = -

As a check

Substitute these values into the original equation and if left side equals right side then these are the solutions.

32 - 162 × ( - )² = 32 - 162 × = 32 - 32 = 0

32 - 162 × ()² = 32 - 32 = 0

Hence solutions are k = ±

56.6

step-by-step explanation:

the ratio of the perimeters is equal to the scale.

the ratio of the areas is equal to the square of the scale.

34 / 20 = k

a / 19.6 = k²

substituting:

a / 19.6 = (34 / 20)²

a = 19.6 (34 / 20)²

a ≈ 56.6