Answer:
150
Step-by-step explanation:
Triangle ADB is a right angle triangle
Use Pythagorean theorem to find out the length of AD
[tex]c^2=a^+b^2[/tex]
[tex]a=16, hypotenuse(c)=20[/tex]
Plug in the values and find out b
[tex]20^2=16^+b^2[/tex]
[tex]400= 256 +b^2[/tex]
Subtract 256 from both sides
[tex]144=b^2[/tex]
Take square root on both sides
[tex]b=12[/tex]
The length of AD is 12
Now we find length of CD using pythagorean theorem
[tex]c^2=a^+b^2[/tex]
[tex]b=12, hypotenuse(c)=15[/tex]
Plug in the values and find out b
[tex]15^2=a^2+12^2[/tex]
[tex]225= 144+a^2[/tex]
Subtract 144 from both sides
[tex]81=a^2[/tex]
Take square root on both sides
[tex]b=9[/tex]
Length of CD = 9
Length of CB = 9+16=25
Area of the triangle ABC= [tex]\frac{CB*AD}{2}[/tex]
=[tex]\frac{25*12}{2}=150[/tex]
