Question

23. ABCD is a trapezium, in which AD and BC are
parallel. If the four sides AB, BC, CD and DA are
respectively 8, 10, 12 and 16, then find the
magnitude of the sum of the squares of the two
diagonals.

Answer 1

Step-by-step explanation:

for finding magnitude of diagonal AB AND BC

=√AB^2+BC^2

$\sqrt{(10 { }^{2} } + 12 {}^{2} )$

$\sqrt{100 + 144}$

$\sqrt{244}$

let's take next diagonal asBC+CD

$\sqrt{(12 {}^{2} } + 16 {}^{2} )$

$\sqrt{144 + 256}$

$\sqrt{400}$

$20$

next diagonal is DC+AD

find the magnitude as usual like AC+BC and DC+ AD

as it is not mentioned particular diagonal therefore we have to take magnitude of all the possible two diagonals