Question

A pen in the shape of an isosceles right triangle with legs of length x ft and hypotenuse of length h ft is to be built. If fencing costs $ 4 divided by ft for the legs and $ 16 divided by ft for the​ hypotenuse, write the total cost C of construction as a function of h.

Answer 1

Answer:

$\frac{8h}{\sqrt{2}} + 16h$

Step-by-step explanation:

First we need to compute the side length as a function of h

So x be the side length of the right isosceles triangle, in Pythagorean formula we have

$x^2 + x^2 = h^2$

$2x^2 = h^2$

$x = \frac{h}{\sqrt{2}}$

The cost for the legs is

$C_l = 4*2x = \frac{8h}{\sqrt{2}}$

The cost for the hypotenuse is

$C_h = 16h$

So the total cost in term of h is

$C = C_l + C_h = \frac{8h}{\sqrt{2}} + 16h$