Question

A rectangular play area is twice as long as it is wide. if you increase the length by 4m and decrease the width by 3m, the new area will be 532m². Determine the dimensions of the original rectangle.​

Answer 1

Answer: 34 m and 17 m

Explanation:

Let the wide is x >0

Hence, the long is 2x >0

Thus,

(2x+4)(x-3)=532

2x(x)+4(x)-2x(3)-4(3)=532

2x²+4x-6x-12=532

2x²-2x-12=532

2x²-2x-12-532=532-532

2x²-2x-544=0

Divide both parts of the equation by 2:

x²-x-272=0

x²-17x+16x-272=0

x(x-17)+16(x-17)=0

(x-17)(x+16)=0

x-17=0

x-17+17=0+17

x=17 m ∈(x>0)

x+16=0

x+16-16=0-16

x=-16 m ∉(x>0)

2x=2(17)

2x=34 m