Cynthia besch wants to buy a rug for a room that is 23ft wide and 26ft long. She wants t ok leave a uniform strip of floor around the rug. She can only afford to buy 270 square feet of carpeting. What dimensions should the rug have?

Step-by-step explanation:

Given: Area of rug= 270 ft²

           Cynthia besch wants to buy a rug for a room that is 23ft wide and 26ft long.

Let´s assume the uniform strip size of floor around rug be "x".

As given, Cynthia wants to leave a uniform strip of floor around the rug.

Considering the shape of rug as rectangle.

∴ Rug dimension will be

We know, area of rectangle=

Forming an equation for area of rug.

⇒

Now solving the equation to find the dimension of rug.

Using distributive property of multiplication.

⇒

⇒

Subtracting both side by 270

⇒

using quadratic formula to solve the equation.

 Formula:

∴ In the expression , we have a= 4, b= -98 and c= 328.

Now, subtituting the value in the formula.

=

=

Opening parenthesis.

=

= \frac{98\pm \sqrt{4356}}{8}

We know 66²=4356  and √a²=a  or -a

=

=

=

∴ Value of x will be either 20.5 ft or 4 ft

Ignoring decimal value, therefore taking value of x as 4 ft.

Subtituting the value of x to find the dimension of rug.

Width of rug=

⇒ Width of rug=

⇒ Width of rug=

Next, Length of rug=

⇒ Length of rug=

⇒ Length of rug=

Hence, dimension of rug is

answer: -8.2562234e+13