SOLUTION: 1. A right triangle has one leg one fourth as long as the other. Find a function that models its perimeter P in terms of the length s of the shorter leg only (ie P(s) =....). Th

Algebra ->  Functions -> SOLUTION: 1. A right triangle has one leg one fourth as long as the other. Find a function that models its perimeter P in terms of the length s of the shorter leg only (ie P(s) =....). Th      Log On


   

Question 1194580: 1. A right triangle has one leg one fourth as long as the other. Find a function that models its perimeter P in terms of the length s of the shorter leg only (ie P(s) =....).
The legs of a right triangle are the two sides that form the right angle.
You may want to draw a diagram for this, but we want P as a function of s only.

2. Find the Domain and Range of the function f(x) = LaTeX: \frac{x-1}{x+3}.
You will need to find the inverse function f-1(x) in order to get your answer.
a) Domain of f. Explain why.
b) Range of f. Explain why.
c) What would be the Range of f-1(x)? Explain why.
Answer by ikleyn(52800) About Me  (Show Source):
You can put this solution on YOUR website!
.

        Problem 1


Shortest leg is s units long;  longer leg is 4s units long.


The hypotenuse is  sqrt%28s%5E2+%2B+%284s%29%5E2%29 = sqrt%2817s%5E2%29 = s%2Asqrt%2817%29 units long.


The perimeter is  P = s + 4s + s%2Asqrt%2817%29 = 5s + s%2Asqrt%2817%29  units long.     ANSWER

Solved and explained.


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You posted your question to me . . . Below is the answer.


The problem asks to find the perimeter in terms of shortest leg.

The problem also says that one leg is one fourth as long as the other.

It makes it clear that if we denote the shortest leg as  " s ",  then the other leg is  4s.


After that,  the solution goes smoothly as in my post above.


This my clarification is from the area of  OBVIOUS  facts,  isn't it ?