Answer
length $5$ yards, width $3$ yards.
Work Step by Step
Step 1. Assume the length is $x$ yards; then the width would be $2x-7$ yards.
Step 2. The area of the room is given by $x(2x-7)=15$; we have $2x^2-7x-15=0$
Step 3. Factor the equation to get $(2x+3)(x-5)=0$; choose the positive solution to get $x=5$ yards.
Step 4. Thus the length is $5$ yards and the width is $3$ yards.
