Question

A triangle has a perimeter of 90 centimeters write and use a linear system

Answer 1

We are given sides of the triangle by expression

First side : n

Second side : m = 5n-5.

Third side : l = 5/4 m - n.

Perimeter is 90.

Therefore, first equation could be set :

n +m +l = 90   --------------equation(1)

Second equation would be

m = 5n-5        --------------equation(2)

Third equation would be

l = 5/4 m - n   --------------equation(3)

Let us solve the system of equations by substitution.

Substituting m = 5n-5 and l = 5/4 m - n in first equation.

We get

n +5n-5 +5/4 m - n= 90

Now, substituting m = 5n-5 in above equation we get

n +5n-5 +5/4 (5n-5) - n= 90

5n + 25n/4 -5 - 25/4 =90

5n + 6.25n -5-6.25 = 90.

11.25n-11.25 = 90

Adding 11.25 on both sides, we get

11.25n-11.25+11.25 = 90+11.25

11.25n = 101.25.

Dividing both sides by 11.25, we get

n=9.

Plugging n=9 in 2nd equation.

m = 5(9)-5 = 45 -5 = 40.

Plugging n=9 and m=40 in first equation, we get

9 +40 +l = 90

49 +l = 90.

Subtracting 49 from both sides, we get

49-49 +l = 90-49

l = 41.

Therefore, sides are of lengths l = 41, m= 40 and n=9.