A rectangular garden 25 feet by 50 feet is increased on all sides by the same amount. Its area increases 400 square feet. By how much is each dimension increased?

Question

Help please I don’t get it

Answer 1

Let's say that each side of the garden is increased by x feet.

Original area = 25*50=1250 sq ft,

new area=1250+400=1650=(x+25)(x+50).

So x^2+75x+1250=1650; x^2+75x-400=0=(x-5)(x+80). So x=5 or -80. We reject -80 because we can't have a negative length, so the extension is 5 feet.

The new size of the garden is 30 by 55 and the area is 1650 sq feet, 400 sq ft more than before.