Question 94008
Call the one side x inches
.
Then another side is 1 inch smaller so it is x - 1 inches.
.
And a third side is 1 inch longer so it is x + 1 inches.
.
The perimeter is the sums of the lengths of the three sides. So we can add up the three sides
to get:
.
{{{x + x - 1 + x + 1}}}
.
Note that the -1 and the +1 cancel each other. So what you are left with is:
.
{{{x + x + x = 3x}}}
.
as being the sum of the three sides. But the sum of the three sides is 17 inches according to
the problem.
.
Therefore, we have:
.
{{{3x = 17}}}
.
You can then solve for x by dividing both sides by 3 to get:
.
{{{x = 17/3}}}
.
On side is 1 inch smaller than that, but 1 inch is the same as {{{3/3}}} inches. So we can
subtract {{{3/3}}} inches from {{{17/3}}} inches to find that this second side has a 
length of {{{17/3 - 3/3 = (17-3)/3 = 14/3}}} inches.
.
And the third side is 1 inch or {{{3/3}}} inches longer than x. So the third side is
given by:
.
{{{17/3 + 3/3 = (17+3)/3 = 20/3}}} inches.
.
And that's the answer. The three sides are {{{14/3}}}, {{{17/3}}}, and {{{20/3}}}.
.
You can check this answer by adding the three sides over their common denominator of 3
to get:
.
{{{ (14+17+20)/3 = 51/3 = 17}}} inches
.
So our answer checks.
.
Hope this helps you to understand the problem.
.