Answer:
The length of the three sides are 18, 29 and 33
Step-by-step explanation:
Let x represent the first side
Let y represent the second side
Let z represent the third side
The perimeter of the triangle is 80cm, which means adding the length of the three sides i.e.
x + y + z = 80cm ......... (eqn 1)
The first side (x) is 7cm shorter than two times (×2) the second side (y) i.e.
x = 2y - 7 ............ (eqn 2)
The third side (z) is 4 cm longer than the first
side (x) i.e.
z = 4 + x ................. (eqn 3)
If x + y + z = 80
We substitute eqn 3 for z
= x + y + 4 + x = 80
= 2x + y + 4 = 80
Next, we substitute eqn 2 for x;
= 2(2y-7) + y + 4 = 80
= 4y - 14 + y + 4 = 80
= 5y - 10 = 80
= 5y = 80 + 10
= 5y = 90
y = 18
If y = 18, we substitute the value of y in eqn 2;
x = 2(18) - 7
x = 36 - 7
x = 29
If x = 29 and y = 18, we substitute both values into eqn 1;
x + y + z = 80
= 29 + 18 + z = 80
= 47 + z = 80
= z = 80 - 47
z = 33
Thus; x, y and z representing the three sides are 29, 18 and 33 respectively.
