Answer:
75 cm²
Explanation:
You want to know the area of a piece of glass 3 times as long as it is wide, if reducing each dimension by 2 cm makes it have an area of 39 cm².
Factors
Assuming the glass has integer dimensions, we note that 39 = 3 × 13, and that increasing these factors by 2 gives two factors that have a ratio of 3:
(3+2) : (13+2) = 5 : 15 = 1 : 3
The original glass was 15 cm long and 5 cm wide, so had an area of ...
A = LW
A = (15 cm)(5 cm) = 75 cm²
The area of the original glass was 75 cm².
__
Additional comment
We could write a quadratic equation to find the width of the original glass:
(w-2)(3w-2) = 39
3w² -8w +4 = 39 . . . . . eliminate parentheses
3w² -8w -35 = 0 . . . . . . put in standard form
There are several ways we could solve this. One way is to factor it.
We're looking for factors of 3·35 = 105 that differ by 8. They are 15 and 7, so the factorization of this is ...
(3w +7)(3w -15)/3 = 0
(3w +7)(w -5) = 0 ⇒ w = 5 . . . . . the glass was 5 cm by 15 cm
<95141404393>