Question

The area of a rectangular room is 238 square feet. The width is 3 feet less than the length. Find the dimensions of the room.

Answer 1

Length= 17 ft; Width= 14 ft

Explanation:

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

Answer 2

Explanation:

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