Answer:
Dimension of rug is
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.
∴ 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 is 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