3 years ago

8----------------------)

Mathematics

1 answer:

Zanzabum3 years ago

3 0

Answer:

HAHA is funny good one I thought it was a real question

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An isosceles triangle has a perimeter of 18 cm. Find a function that models its area A in terms of the length of its base b.

IgorLugansk [536]

So.... notice the picture below

now, we know what the "height" or "altitude" is
now, we also know the perimeter is 18cm

so, k + k + b = 18
or 2k + b = 18
thus $\bf k=\cfrac{18-b}{2}$

so... one can say that $\bf \textit{area of a triangle}=A=\cfrac{1}{2}bh\qquad 
\begin{cases}
b=b
\\\\
h=\sqrt{k^2-\left( \frac{b}{2} \right)^2}
\\\\
h=\sqrt{k^2-\frac{b^2}{4}}\\
--------------\\
k=\frac{18-b}{2}\qquad thus\\
--------------\\
h=\sqrt{\left( \frac{18-b}{2} \right)^2-\frac{b^2}{4}}
\end{cases}\\\\
-----------------------------\\\\
A=\cfrac{1}{2}\cdot b\cdot \sqrt{\left( \frac{18-b}{2} \right)^2-\frac{b^2}{4}}$

and you can simplify it if you wish.. not sure you have to