Question

A square is inscribed in a right triangle with leg lengths 6 and 8 such that they have a common right angle. find the square's side length.

Answer 1

The square's side length is 24/7 or 3.428 units if the square is inscribed in a right triangle with leg lengths 6 and 8 such that they have a common right angle.

What is a right-angle triangle?

It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.

First we have to find the line that goes through the points (0, 6) and (8, 0)

(y - 0) = (0-6)/(8-0)(x-8)

y = (-6/8)[x - 8]

Plug y = x

x = (-6/8)[x - 8]

After solving:

x = 24/7 or 3.428

y = 24/7 or 3.428

Thus, the square's side length is 24/7 or 3.428 units if the square is inscribed in a right triangle with leg lengths 6 and 8 such that they have a common right angle.

Learn more about the right angle triangle here:

brainly.com/question/3770177

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