Question

Analyze the diagram below and complete the statement that follows.

The area of triangle ABC is _____.

A. 60
B. 65
C. 130
D. 150

Answer 1

D. 150 should be your answer.

Answer 2

150

Explanation:

Triangle ADB is a right angle triangle

Use Pythagorean theorem to find out the length of AD

`c^2=a^+b^2`

`a=16, hypotenuse(c)=20`

Plug in the values and find out b

`20^2=16^+b^2`

`400= 256 +b^2`

Subtract 256 from both sides

`144=b^2`

Take square root on both sides

`b=12`

The length of AD is 12

Now we find length of CD using pythagorean theorem

`c^2=a^+b^2`

`b=12, hypotenuse(c)=15`

Plug in the values and find out b

`15^2=a^2+12^2`

`225= 144+a^2`

Subtract 144 from both sides

`81=a^2`

Take square root on both sides

`b=9`

Length of CD = 9

Length of CB = 9+16=25

Area of the triangle ABC=
`(CB*AD)/(2)`

=
`(25*12)/(2)=150`