One of the legs of a right triangle has length 4 cm. express the length of the altitude perpendicular to the hypotenuse as a function of the length of the hypotenuse

This is about division of a right angle triangle.

y =  √(h² - 4²)

Longer leg = √(h² - 4²)

y/4 = (√(h² - 4²))/h

Thus, the altitude as a function of the Length of the hypotenuse gives;

y =

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Without loss of generality, we can think of the 4 cm leg of the triangle as being the short leg. It is also the hypotenuse of the smallest of the similar triangles created by the altitude (x). If h represents the hypotenuse of the triangle, then similarity tells us the ratio of the "long" leg to the hypotenuse is the same for the smallest and largest triangles.

... x/4 = √(h²-4²)/h

Then the altitude (x) as a function of the hypotenuse (h) is ...

... x = (4/h)×√(h²-16)

the answer will be b x² +x-1

step-by-step explanation: