Aright triangle with a perimeter 24 has sides of lengths 2x, (2x + 2) and (2x + 4). what is the area of the triangle?
a) 18
b) 21
c) 24
d) 28

C) 24

Step-by-step explanation:

1. Since the perimeter of a triangle is the sum of its three sides, you can write the following expression, solve for x and get the value of each side.

2. So, replacing the value of x, you can calculate the values of each side of the triangle:

First side:

Second side:

Third side:

As the larger side is the third one, it is the hypotenuse. So, the base and the  height.

3. The formula to find the area of the right triangle is given by the expression:

Where b is the base and h is the height of the triangle, so replacing the values we found, we have the following:

Therefore the answer is C) 24

(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