Problema Solution
In a trapezium, the two non parallel sides are equal in length, each being of 5 units. The parallel sides are at a distance of 3 units apart. If the smaller side of parallel sides is of length 2 units, then the sum of the diagonals of the trapezium is ?
Answer provided by our tutors
make a good drawing and use Pythagorean Theorem couple of times
both of the diagonals in this trapezium are equal thus it is sufficient to find the length of one of the diagonals:
d^2 = (2 + √(5^2 + 3^2))^2 + 3^2
d^2 = (2 + 4)^2 + 9
d^2 = 36 + 9
d^2 = 45
d = √45
d = 3√5
the sum of the diagonals of the trapezium is d + d = 2d = 2*3√5 = 6√5 units or 13.42 units approximately.