Arectangular garden measures 40 yards by 35 yards. a lawn of uniform width surrounds the garden and has an area of 316 square yards. find the width of the lawn that surrounds the garden.

The lawn area of uniform width can be written as follows:
 A = (40 + 2x) * (35 + 2x) - (40) * (35)
 Where,
 x: width of the lawn
 Substituting the value of the area we have:
 316 = (40 + 2x) * (35 + 2x) - (40) * (35)
 Rewriting:
 316 = 1400 + 80x + 70x + 4x ^ 2 - 1400
 Rewriting we have:
 4x ^ 2 + 150x - 316 = 0
 Solving the polynomial we have:
 x1 = - 79/2
 x2 = 2
 Taking the positive root we have that the grass width des:
 x = 2 yards
 
 The width of the lawn that surrounds the garden is:
 x = 2 yards