SOLUTION: one side of a triangle is 1 in. longer than the shortest side and is 1 in. shorter than the longest side. the perimeter is 17 in. what is dimensions of triangle?

Question 94008This question is from textbook
: one side of a triangle is 1 in. longer than the shortest side and is 1 in. shorter than the longest side. the perimeter is 17 in. what is dimensions of triangle?
This question is from textbook

Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
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:
.

.
Note that the -1 and the +1 cancel each other. So what you are left with is:
.

.
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:
.

.
You can then solve for x by dividing both sides by 3 to get:
.

.
On side is 1 inch smaller than that, but 1 inch is the same as inches. So we can
subtract inches from inches to find that this second side has a
length of inches.
.
And the third side is 1 inch or inches longer than x. So the third side is
given by:
.
inches.
.
And that's the answer. The three sides are , , and .
.
You can check this answer by adding the three sides over their common denominator of 3
to get:
.
inches
.
So our answer checks.
.
Hope this helps you to understand the problem.
.
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