Question

Analyze the diagram below and complete the statement that follows.

Answer 1

D. 150 should be your answer.

Answer 2

Answer:

150

Step-by-step 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= $\frac{CB*AD}{2}$

=$\frac{25*12}{2}=150$