Question

The side of a square increased by 2 the area becomes 100
a)if the initial side is x then what is the new side length? b)write the equation connecting side length and area C)find the initial side length and new side length :

Answer 1

Given :

• Initial side = x cm
• New side = x + 2 cm
• Area = 100 cm²

Solution :

$\boxed{\sf Area \: of \: square = {a}^{2}} \\ \\ \sf {(x + 2)}^{2} = 100 \\ \\ \sf {x}^{2} + 4x + 4 = 100 \\ \\\sf {x}^{2} + 4x - 96 = 0 \\ \\\sf {x}^{2} - 8x + 12 gx- 96 = 0 \\ \\\sf x(x - 8) + 12(x - 96) = 0 \\ \\ (x - 8)(x + 12) \\ \\\boxed{\sf x = 8} \\ \boxed{ \sf x = - 12}$

Side can't be negative so side of square is 8 cm

$\implies\sf Initial \:side = 8 cm \\ \\</p><p>\implies \sf New \:side = 8 + 2 = 10 cm$