MHB Is the perimeter of a right triangle equal to its area? (Part 2)

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In the discussion, a right triangle is defined with legs u and v, and hypotenuse w. The values of u, v, and w are expressed in terms of variables m and n. The objective is to demonstrate that the area of the triangle, calculated as (1/2)(uv), equals the perimeter, represented by u + v + w. The participants confirm that the calculations involve multiplying u and v by 1/2 and then adding the lengths to verify the equality. The exercise aims to illustrate that the perimeter and area of this specific right triangle are numerically equal.
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A right triangle is given. One leg is u units and the other leg is v units. The hypotenuse is given to be w units.

If u = [2(m + n)]/n, v = 4m/(m - n), and
w = [2(m^2 + n^2)/(m - n)n, show that

(1/2)(uv) = u + v + w

I must multiply u times v times (1/2), right? I then must add u + v + w. The right side must equal the left, right?

This exercise will show that the perimeter is numerically equal to the area.
 
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RTCNTC said:
I must multiply u times v times (1/2), right? I then must add u + v + w. The right side must equal the left, right?
Yes.
 
Evgeny.Makarov said:
Yes.

Cool.
 

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