Question

Let a*b denote the length of the hypotenuse of a right angle triangle whose remaining two sides have length a, b. If (12*16)*k=25 then find the value of k2.

Answer 1

If length of base and altitude of a right triangle is a and b, then length of hypotenuse is given that a*b
but by pythogorus theorem we know that length of hypotenuse is root(a^2+b^2)
so by comparing this a*b=root(a^2+b^2)
so 12*16=root(12^2+16^2)
=root(144+256)
=20
20*k=25(given
​​​​​​)
so root(20^2+k^2)=25
root(400+k^2)=25
squre both sides
then 400+k^2=625
k^2=625-400=225