problem solving

Question

If each of the sides of a square is lengthened by 6cm, the area becomes 144cm2. Find the length of a side of the original square.

Answer 1

Length of a side of the original squre = a cm

Area of squre(A ) = a ^2 cm^2

If each side of squre is lengthened by 6cm ,

Then length of the squre = a + 6 cm

Then it's area becomes A  = 144 cm^2

 (a +6)(a +6) =144

a ^2 + 6a  + 6a  + 36 = 144

a ^2 + 12a  + 36 = 144

a ^2 + 12a  + 36 - 144 = 0

a ^2 + 12a  - 108 = 0

a ^2 + 18a  - 6a  - 108 = 0

a (a  + 18) - 6(a  + 18) = 0

(a  + 18) (a - 6) = 0

Apply zero product property.

a + 18 = 0 and a  - 6 = 0

a  = - 18 and a  = 6

Length is always positive so a  = 6.

Length of a side of the original squre = 6cm.