The first side of the triangle is 6 cm longer than the second side. The third side is 4 cm shorter than the first side. How long is each side if the perimeter of the triangle is 29 cm?
Answers
Given :
- First side of the triangle = Second Side of the triangle + 6.
- Second side of the triangle = First side of the triangle - 4.
- Perimeter of the triangle = 29 cm.
To find :
The measure of each side of the triangle.
Solution :
Let the second side of the triangle be x cm.
So according to the question,
- First side of the triangle = (x + 6) cm.
- Third side of the triangle = (x + 6) - 4 cm.
We know the formula for perimeter of a triangle i.e,
⠀⠀⠀⠀⠀⠀⠀⠀⠀P = a + b + c
Where :
- P = Perimeter
- a = First side
- b = Second Side
- c = Third side
Now by using the above formula and substituting the values in it, we get :
==> P = a + b + c
==> 29 = (x + 6) + x + (x + 6) - 4
==> 29 = (x + x + x) + (6 + 6 - 4)
==> 29 = 3x + 8
==> 29 - 8 = 3x
==> 21 = 3x
==> 21/3 = x
==> 7 = x
∴ x = 7 cm.
Hence the value of x is 7 cm.
Now by substituting the value of x in the sides of the triangle (in terms of x) , we get :
- First side of the triangle :-
==> a = x + 6
==> a = 7 + 6
==> a = 13
∴ a = 13 cm.
Hence the first side of the triangle is 13 cm.
- Second side of the triangle :-
==> b = x
==> b = 7
∴ b = 7 cm
Hence the second side of the triangle is 7 cm.
- Third side of the triangle :-
==> c = (x + 6) - 4
==> c = (7 + 6) - 4
==> c = 13 - 4
==> c = 9
∴ c = 9 cm.
Hence the third side of the triangle is 9 cm.