Answer:
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.
[tex]2x+(2x+2)+(2x+4)=24\\2x+2x+2+2x+4=24\\6x+2+4=24\\6x+6=24\\6x=24-6\\6x=18\\x=\frac{18}{6}\\x=3[/tex]
2. So, replacing the value of x, you can calculate the values of each side of the triangle:
First side:
[tex]2x=2(3)=6[/tex]
Second side:
[tex](2x+2)=(2(3)+2)=6+2=8[/tex]
Third side:
[tex](2x+4)=(2(3)+4)=6+4=10[/tex]
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:
[tex]A=\frac{b*h}{2}[/tex]
Where b is the base and h is the height of the triangle, so replacing the values we found, we have the following:
[tex]A=\frac{8*6}{2}[/tex]
[tex]A=\frac{48}{2}[/tex]
[tex]A=24[/tex]
Therefore the answer is C) 24
