Question

The area of a parallelogram is 486 square cm. The sum of its bases is 54 cm. Each slanted side measures 14 cm. What is its height?

Answer 1

10.783 cm nearly. The other side of the parallelogram is (rounded to 5-sd ) is 45.071 cm.

Explanation:

Let a be the other side, h and k the altitudes and `alpha` the

angle between the adjacent sides..Now,

Area = a h = 14 k = 486. So, k = 243/7.

`sin alpha = h / 14 and cos alpha = ( 54 - a ) /14 ) = (54-486/h)/14`

Using `sin^2alpha + cos^2alpha = 1`,

`(h/14)^2 + ((54-486/h)/14)^2 = 1`

This is a biquadratic in `h`. .

Graphical solutions near 7.5 and 10.5to the altitude h:.
graph{y-((x/14)^2 + ((54-486/x)/14)^2 - 1)=0[5 15 -1 1]}

Trial an error root-bracketing gives the altitude near 10.5 as 10.783

cm.

graph{y-((x/14)^2 + ((54-486/x)/14)^2 - 1)=0[10.78 10.785 -0.0001 0.0001]}

As a < 54, the corresponding h > 486/54 = 9. So, the second

solution near 7.5 is inadmissible.