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

In summary, given a right triangle with one leg of u units and another leg of v units, and a hypotenuse of w units, if u = [2(m + n)]/n, v = 4m/(m - n), and w = [2(m^2 + n^2)/(m - n)n, then (1/2)(uv) = u + v + w. This exercise shows that the perimeter is numerically equal to the area.
  • #1
mathdad
1,283
1
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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  • #2
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.
 
  • #3
Evgeny.Makarov said:
Yes.

Cool.
 

What is the Pythagorean theorem?

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

How do you find the missing side in a right triangle?

To find the missing side in a right triangle, you can use the Pythagorean theorem or apply trigonometric ratios (sine, cosine, tangent) depending on the given information.

What is a special right triangle?

A special right triangle is a right triangle that has angles that correspond to specific trigonometric ratios, making it possible to find the lengths of the sides without using the Pythagorean theorem.

What is the difference between a right triangle and an oblique triangle?

A right triangle has one angle that measures 90 degrees, while an oblique triangle has all three angles that measure less than 90 degrees.

How do you determine if a triangle is a right triangle?

A triangle is a right triangle if one of its angles measures 90 degrees. This can also be determined by using the Pythagorean theorem or checking if the sides follow the Pythagorean relationship.

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