Question

1) Lena's garden is a square with sides of length x meters. Next spring, she plans to make it rectangular by lengthening one side 5 meters and shortening the other side by 5 meters. a) What algebraic expression represents the new area? b) By how much will the area of the new garden differ from that of the old garden​

Answer 1

a) Algebraic expression for new area = (x + 5)(x - 5 )

b) New area will be 25 square meters less than old area

Explanation:

Lena' s square garden with side x has area x times x or x² square meters

If one side is lengthened by 5 meters that side becomes x + 5 meters

If the other side is shortened by 5 meters that side becomes x - 5 meters

New area = (x + 5)(x - 5 )

Using the identity(a + b)(a - b) = a² - b² we get

(x + 5)(x - 5 ) =x² - 5²

= x² - 25

Area difference square - rectangle =
x² - (x² - 25) = x² - x² + 25

= 25

So the area will decrease by 25 square meters