Chapter 4.9, Problem 6P

To determine

To calculate: the area of each room.

Answer to Problem 6P

400 ft²

Explanation of Solution

Given:

Two rooms of a house have equal area one room is square & other is rectangle

Width of the rectangular room is 4 ft narrower than square room

length of the rectangular room is 5 ft longer than square room

Calculation:

Let width of the square room= $x$ ft

Let length of the square room = $x$ ft

Now area of the square room = $x^2$ ft

Let width of the rectangular room= $\left(x-4\right)$ ft

Let length of the rectangular room = $\left(x+5\right)$ ft

Area of rectangular room $\left(x-4\right)\left(x+5\right)$ ft²

Equating both the areas

  $\begin{array}{l}{x}^2=\left(x-4\right)\left(x+5\right)\\ x^2=x^2+5x-4x-20\\ 0=x-20\\ x=20\end{array}$

width of the square room= $20$ ft

length of the square room = $20$ ft

area of the square room = ${20}^2=400$ ft²

width of the rectangular room= $16$ ft

Let length of the rectangular room = $25$ ft

Area of rectangular room $16\times 25=400$ ft²

Now area of both the room is 400 ft²