the measure of pair of adjacent sides of a parallelogram are 15cm and 20cm.if the length of one diagonals is 25cm find the area of the parallelogram.
To find the area of a parallelogram, we can use the formula A = base x height, where the base is the length of one of the sides and the height is the length of the perpendicular distance between the base and the opposite side.
In this case, we are given the lengths of both adjacent sides, 15 cm and 20 cm, and the length of one diagonal, 25 cm.
First, we need to find the length of the other diagonal, which is also the height of the parallelogram. To do this, we can use the fact that the diagonals of a parallelogram bisect each other.
Let the length of the other diagonal be x. We can consider the parallelogram as two congruent triangles formed by the diagonals. Using the Pythagorean theorem, we can set up an equation:
15^2 + (x/2)^2 = 25^2
Simplifying the equation, we have:
225 + x^2/4 = 625
x^2/4 = 625 - 225
x^2/4 = 400
x^2 = 1600
x = √1600
x = 40 cm
So, the length of the other diagonal, or the height of the parallelogram, is 40 cm.
Now we can calculate the area of the parallelogram:
A = base x height
A = 20 cm x 40 cm
A = 800 cm^2
Therefore, the area of the parallelogram is 800 square centimeters.
well, let's try the 20 on the bottom and the 15 sloping up toward the right. Try the diagonal connecting the two right ends.
draw altitude h
that divides the base into x and (20-x)
x^2+ h^2 = 225 so h^2 = 225-x^2
(20-x)^2 + h^2 = 625
-----------------------
400 -40 x + x^2 +(225-x^2)=625
that gives x = 0 so try the 25 as the long diagonal
x^2+h^2 = 225 again
but
(x+20)^2 + h^2 = 625
x^2 + 40 x +400 + 225-x^2 = 625
40 x = again
so we have to bite the bullet and let x = 0
That means that our parallelogram is a RECTANGLE
area = 20*15 = 300 cm^2
:)
(if we were smart we would have noticed that we had a 3,4,5 right triangle )