top button
Flag Notify
    Connect to us
      Facebook Login
      Site Registration Why to Join

    Get Free Puzzle Updates

Facebook Login
Site Registration

The lengths of two adjacent sides of a parallelogram are 8 and 15. Find the sum of squares of lengths its diagonals.

0 votes
100 views

The lengths of two adjacent sides of a parallelogram are 8 and 15, respectively. Find the sum of squares of the lengths of the two diagonals.

Parallelogram

posted Jan 17, 2017 by anonymous

Share this puzzle
Facebook Share Button Twitter Share Button LinkedIn Share Button

1 Answer

0 votes

Diagnals can be found out using cosine law but the angles will be unknown as shown below.

D1^2 = 8^2 + 15^2 - 2(8*15*Cos A) [A is the smaller angle here and D1 the smaller diagnal ]

D2^2 = 8^2 + 15^2 - 2 (8*15* Cos (180-A)) [all the angles in a parallelogram add upto 360 degree.]

Since D1^2 + D2^2 is the needed answer adding the above to gets us an answer = 578 units. [ because the terms with angles cancel each other as Cos (180-A) = -Cos (A).]

answer Jan 17, 2017 by Tejas Naik



Similar Puzzles
–1 vote

A given parallelogram has sides measuring 7 and 9, and both its diagonals have integer lengths. Find the sum of all possible products of the lengths of the diagonals.

0 votes

Trapezoid as shown has two parallel sides with length 5 and 15 & two diagonals with length 12 and 16. What is its area?

enter image description here

–1 vote

If the length of two sides of a right angled triangle measured in inches are prime numbers, and it has two adjacent sides of 12 and 13 inches long, how long must the third side be?

Contact Us
+91 9880187415
sales@queryhome.net
support@queryhome.net
#280, 3rd floor, 5th Main
6th Sector, HSR Layout
Bangalore-560102
Karnataka INDIA.
QUERY HOME
...