A function that gives the length of the hypotenuse of an isosceles right triangle with side length s is given by h(s)=s√2 and the length of the side of the triangle is approximately 4.24 inches.
The hypotenuse of a right angled triangle is defined as the longest side of the triangle. The hypotenuse is also located opposite the right angle.
From the Pythagorean Theorem we know that for a right angled triangle, the sum of the square of the legs of the triangle is equal to the square of the hypotenuse.
Given legs of the right triangle is s. Let us consider a function h(s) for the hypotenuse.
Therefore we can define the function h(s) as
h(s)=s√2
The inverse of the function can be written as
y=s√2
or, s=y²/2
Hence the inverse function is:
h⁻¹(s)=s²/2
Now for hypotenuse = 6 inches.
Each side can be calculated using the inverse function h⁻¹(s)=s²/2.
s=6÷√2
or, s=4.242...
Hence the length of the side of the triangle is approximately 4.24 inches.
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