Towns-A-B-C-and-D-are-located-on-the-vertices-of-a-square-whose-area-is-1000km-2-There-is-a-straight-line-highway-passing-through-the-centre-of-the-square-but-not-through-any-of-the-towns-Find-the-

Question Number 111278 by Aina Samuel Temidayo last updated on 03/Sep/20

Towns A, B, C and D are located on

the vertices of a square whose area is

{1000 km}^{2} . There is a straight line

highway passing through the centre of

the square but not through any of the

towns . Find the sum of the squares

of the distances of the towns to the

highway .

Answered by ajfour last updated on 03/Sep/20

Commented by Aina Samuel Temidayo last updated on 03/Sep/20

Solution please ?

Commented by ajfour last updated on 03/Sep/20

p + q = a \sin θ

p - q = a \cos θ

d_{A}^{2} + d_{B}^{2} + d_{C}^{2} + d_{D}^{2} = q^{2} + p^{2} + q^{2} + p^{2}

= 2 (p^{2} + q^{2}) = {(a \sin θ)}^{2} + {(a \cos θ)}^{2}

= a^{2} = 1000 {k m}^{2} .

Commented by Aina Samuel Temidayo last updated on 03/Sep/20

Ok . Thanks . I really appreciate that .