Question

A square garden is surrounded by a 2 feet wide walkway on each side. The area of the garden and the walkway is 225 square feet. If the garden is broadened by increasing side of the garden by 5 units then what will be the area of the garden?

Answer 1

Answer:

400 square units

Step-by-step explanation:

let the side of square garden be x

width of pathway is 2 ft

area of both is 225 square ft

${(x + 4)}^{2} = 225 \\ {x}^{2} + 8x + 16 = 225 \\ {x}^{2} + 8x + 16 - 225 = 0 \\ {x}^{2} + 8x - 209 = 0 \\ {x}^{2} + 19x - 11x - 209 = 0 \\ x(x + 19) - 11(x + 19) = 0 \\ (x + 19)(x - 11) = 0 \\ x + 19 = 0 \: \: \: \: x - 11 = 0 \\ x = - 19 \: \: \: \: \: \: \: \: \: x = 11 \\ side \: of \: square \: is \: 11 \: ft \\ side \: of \: garden \: with \: pathway \: is \: 15ft$

garden is broadened by 5 units then side increase to 20 ft

the area will be 20 × 20 = 400sq units