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