The first side of a triangle is three times as long as the second side, and the third side is 50 cm shorter than the first side. Find all sides of triangle if its perimeter is 370 cm.

Step-by-step explanation:

First side = a

Second side = b

Third side = c

a is three times as long as the b (a=3b). C is 50 cm shorter than a (c=50-a)

The perimeter is 370cm (a+b+c=370)

Take and solve for b;

Now b is in terms of a, and c is in terms of a, therefore if we replace in the last equation all these values, we can find a.

Add 50 on both sides.

Multiply by the reciprocal of . The reciprocal of a fraction is the inverted fraction. Therefore it is:

Now replace a in the equation to find b.

Finally, replace a in the equation to find c

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3

step-by-step explanation: