Question

One side of a triangle

is seven inches more
than the first side. The
third side is four inches
less than three times
the first. The perimeter
is 28 inches. Find the
length of the three
sides of the triangle.

Answer 1

As per question,

Let the sides be:

a = first side

b = second side

c = third side

As one side is seven inches more than first side,

b = 7 + a

As the third side is four inches less than three times the fiest, so,

c = 3a - 4

As perimeter is 28 inches,

a + b + c = 28

Now solving for sides,

`a = a \\ = > b = 7 + a \\ = > c = 3a - 4`

So,

`a + b + c = 28 \\ = > a + (7 + a) + (3a - 4) = 28 \\ = > a + 7 + a + 3a - 4 = 28 \\ = > a + a + 3a + 7 - 4 = 28 \\ = > 5a + 3 = 28`

Now subtract,

5a = 25

=> a = 25÷5

=> a = 5

Now as we got value o lengrh of first side, substitute it to the remaining sides.

=> b = 7 + a

=> b = 7 + 5

=> b = 12

And finally,

c = 3a - 4

=> c = 3×5 - 4

=> c = 15 - 4

=> c = 11

Therefore, the three sides are 5 inches, 12 inches and 11 inches