Question

The sum of the squares of the length of all sides of a rectangle is 100. What is the length of a diagonal of the rectangle? EXPLAIN IT WITH CLEAR SOLUTION

Answer 1

let we take length of larger sides &shorter sides be a & b respectivly. here (a2,b2,h2 means square of a b & h respectively )
then,
according to question
a2+a2+b2+b2=100
2(a2+b2)=100
a2+b2=100÷2
a2+b2=50....(1)
if the larger side(a) be perpendicular& the shorter side(b) be base & igonal be the hypotanous (h)
then
h2=p2+b2
h2=a2+b2
h2=50 (fromeq (1))
h=5root2