Question

If the area of the shaded region in the diagram below is 103 square feet, what are the dimensions of the inside rectangle?

Inside Rectangle:
-Length: x-1
-Width: 2x

Outside Rectangle:
-Length: 3x-2
-Width: x+6

Answer 1

Answer:

The dimensions of the inside rectangle are

$Length=4\ ft$

$Width=10\ ft$

Step-by-step explanation:

we know that

The area of the shaded region is equal to the area of the outside rectangle minus the area of the inside rectangle

see the attached figure to better understand the problem

so

$103=(3x-2)(x+6)-(x-1)(2x)\\ \\103=(3x^{2}+18x-2x-12)-(2x^{2}-2x)\\ \\103=3x^{2}+16x-12-2x^{2}+2x\\ \\103=x^{2}+18x-12\\ \\ x^{2}+18x-115=0$  

using a graphing calculator

the solution is

$x=5\ ft$

see the attached figure

Find the dimensions of the inside rectangle

$Length=(5-1)=4\ ft$

$Width=2(5)=10\ ft$