Answer
Length : $5$ yards.
Width: $3$ yards.
Work Step by Step
Let's note the length of the rectangular floor by $x$.
The width of the rectangular floor is $2x-7$.
The area of the rectangular floor is $(x)(2x-7)$.
We are given that the area of the bedroom is $15$ square yards.
Equate both.
$\Rightarrow (x)(2x-7)=15$
Apply the distributive property.
$\Rightarrow x\cdot 2x-x\cdot 7=15$
Simplify.
$\Rightarrow 2x^2- 7x=15$
Subtract $15$ from both sides.
$\Rightarrow 2x^2- 7x-15=15-15$
Add like terms.
$\Rightarrow 2x^2- 7x-15=0$
Rewrite the middle term $-7x$ as $-10x+3x$
$\Rightarrow 2x^2- 10x+3x-15=0$
Group the terms.
$\Rightarrow (2x^2- 10x)+(3x-15)=0$
Factor each group.
$\Rightarrow 2x(x- 5)+3(x-5)=0$
Factor out $(x-5)$.
$\Rightarrow (x- 5)(2x+3)=0$
Set each factor equal to zero.
$x-5=0$ and $2x+3=0$
Isolate $x$.
$x=5$ and $x=-\frac{3}{2}$
Take positive value because $x$ represents a dimension and has to be positive.
Length $x=5$ yrads.
Width $2x-7=2(5)-7=10-7=3$ yards.
