Question

An architect is allowed 70 square yards of floor space to add a small bedroom to a house. Because of the room's design in relation to the existing structure, the length

of the rectangular floor must be 4 yards less than 2 times the width. Find the length and width of the rectangular floor that the architect is permitted.​

Answer 1

set width as a, so length is 2a-4

a(2a-4)=70

2a^2 - 4a = 70

a^2 - 2a = 35

a^2 - 2a + 1 = 36

(a-1)^2 = 36 Because width can not be negative so we only take possitive answer.

(a-1) = 6

a = 7

2(7) - 4

=14-4

=10

Length = 10

Width = 7