Answer:
15 cm
Step-by-step explanation:
The length of the shorter pole can be found by forming and subsequently solving 2 equations.
Start by defining the variables that are going to be used in the working.
Let the original length of the shorter pole be a cm and that of the longer pole be b cm.
'Product' refers to the multiplication operation.
ab= 285 -----(1)
On the other hand, 'sum' refers to the addition operation.
Length of shorter pole after cutting= a -2
Length of longer pole after cutting= b -2
(a -2) +(b-2)= 30
a +b -4= 30
Adding 4 to both sides:
a +b= 30 +4
a +b= 34 -----(2)
From (2):
a= 34 -b -----(3)
Let's solve by substitution:
Substitute (3) into (1):
b(34 -b)= 285
Expand:
34b -b²= 285
b² -34b +285= 0
Factorise:
(b -15)(b -19)= 0
b -15= 0 or b -19= 0
b= 15 or b= 19
Substitute into (1):
a(15)= 285 or a(19)= 285
a= 285 ÷15 or a= 285 ÷19
a= 19 or a= 15
Since a <b, a= 15 and b= 19.
Thus, the length of the shorter pole is 15 cm.
