One of diagonals of a parallelogram is its altitude. what is the length of this altitude, if its perimeter is 50 cm, and the length of one side is 1 cm longer than the length of the other?

Parallelograms have parallel and congruent opposite sides.  

The altitude of the parallelogram is 5 cm

Let:

altitude

perimeter

So, we have:

Let x and y be the sides of the parallelogram; so, we have:

and

This gives:

Divide by 2

Substitute

Subtract 1 from both sides

Divide both sides by 2

Recall that:

See attachment for the illustration of the parallelogram.

From the attached parallelogram, we have:

---- Pythagoras theorem

So, we have:

Collect like terms

Take positive square roots

Hence, the altitude of the parallelogram is 5 cm

Read more about parallelograms at:

link

The sum of adjacent sides is half the perimeter, so is 25 cm. Since the side lengths are consecutive numbers, they are both nearly half of 25 cm. One side is 12 cm, the other is 13 cm.

These lengths, then, are one leg and the hypotenuse of the right triangle that makes up half the parallelogram. The other leg, the altitude, is found using the Pythagorean theorem (or your knowledge of Pythagorean triples). It is

... altitude = √((13 cm)² -(12 cm)²) = √(25 cm²) = 5 cm

The length of the altitude is 5 cm.

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