Question

A rectangular 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.

Answer 1

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
 Answer:
 The width of the lawn that surrounds the garden is:
 x = 2 yards