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n the triangle below, if AC = 17 m, CP =15 m, and AB = 16 m, find the area of the triangle ABC.

N The Triangle Below If AC 17 M CP 15 M And AB 16 M Find The Area Of The Triangle ABC class=

Sagot :

We need to find CB using Pitagora's theorem

PB = AB/2 = 16/2 = 8

So:

[tex]\begin{gathered} CB^2=PB^2+CP^2 \\ CB^2=\text{ 8}^2\text{ + 15}^2 \\ CB^2=\text{ 64 + 225} \\ CB^2=\text{ 289} \\ \sqrt{CB^2=\text{ }\sqrt{289}} \\ CB=\text{ 17} \end{gathered}[/tex]

Now we need to find out the area of the triangle:

[tex]\begin{gathered} A=\text{ }\frac{bxh}{2} \\ A=\frac{16x15}{2} \\ A=\text{ }\frac{240}{2} \\ A=\text{ 120} \end{gathered}[/tex]

The area of the triangle is 120 m^2.

The answer is B. 120m^2.

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