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 are the dimensions of the triangle?

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Answer 1 · 2018-01-03T04:29:52

Measure of the three sides of the triangle #color(blue)((4(2/3), 5(2/3), 6(2/3))#

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The sides are a, b, c.

Given a = b - 1 as also c = b + 1;

Further perimeter #p = a + b + c = 17#

#:. p = 17 = a + b + c = b - 1 + b + b + 1 = 3b#

#b = 17 / 3 = 5 (2/3)#

#:. a = b - 1 = 5 (2/3) - 4 (2/3)#

#c = b + 1 5 (2/3) + 1 6 (2/3)#

Measure of the three sides of the triangle is #color(blue) ((4(2/3), 5(2/3), 6(2/3))#

Answer 2 · 2018-01-03T04:38:02

#4(2)/3#in; #5(2)/3# in.; #6(2)/3# in.

Suppose the shortest side of the triangle = #x# in.
Then the other side is #x+1# in.

Therefore, the longest side = #x+1+1# = #x+2# in.

It is given that the perimeter = 17 in.

and, as perimeter is the sum of all the sides, it can be written in an equation form as:
#x+(x+1)+(x+2)# = 17

or, #3x+3 = 17#
or, #3x = 17-3# =14

or, #x# = #14/3# in. = #4(2)/3#in.(shortest length)

and, #x+1# = #14/3 +1# = #17/3# = #5(2)/3# in. (mid-length)

and, #x+2# = #14/3+2# = #20/3# = #6(2)/3# in. (longest side)