Respuesta :

Americ
L= length
w= width= L-3
A= area= 238 ft^2


LENGTH
Area Formula

A= LW
substitute w value

238= (L)(L- 3)
multiply L by parentheses

238= L^2 - 3L
subtract 238 from both sides

0= L^2 - 3L - 238
factor

0= (L + 14)(L - 17)
set each parentheses equal to 0

0= L + 14
-14= L

OR

0= L - 17
17 ft= L

*Since the measure of a rectangle would not be negative, L= 17 ft

WIDTH
w= L - 3
w= 17 - 3
w= 14 ft


ANSWER: Length= 17 ft; Width= 14 ft

Hope this helps! :)

The length of the room is 17 feet and the width of the rectangle is 14 feet.

Given

The area of a rectangular room is 238 square feet.

The width is 3 feet less than the length.

Let the length of the room be L and the width is W.

The width of the room is L-3.

What is an area of a rectangular room?

The area of the room is given by the product of the length and base.

[tex]\rm Area = Length \times width\\\\[/tex]

Therefore,

The dimension of the room is;

[tex]\rm Area = Length \times width\\\\\\\\238=L\times (L-3)\\\\238=L^2-3L\\\\L^2 - 3L - 238=0\\\\(L + 14)(L - 17)=0\\\\L+14=0, \ \ L=-14\\\\L-17=0, \ \ L=17[/tex]

The value of the length can not be negative then the value of length is 17.

Then,

The width of the rectangle is;

L - 3 = 17-3 = 14

Hence, the length of the room is 17 feet and the width of the rectangle is 14 feet.

To know more about Area click the link given below.

https://brainly.com/question/9541340

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