Question

one side of a rectangle is 20cm. if the other side is decreased by 6cm the diagonal will be decreased by 4cm. find the length of the other side.

Answer 1

let other side of the rectangle be x.
if other side decreased by 6 ---> x-6
u know how to find the diagonal of rectangle ??

Answer 2

[x^{2} +20^{2}=y^{2}]
y=original length of the diagonal
(x-6)^2+20^2=(y-4)^2

Answer 3

so lets isolate one variable from those 2 equations....

Answer 4

y from 1st equation is\(\sqrt{x^2+400}\)
substitute in 2nd eq.:
\((x-6)^2+400=(\sqrt{x^2+400}-4)^2\)
evaluate Right side first and tell what u get...?

Answer 5

okk,u get
\(x^2-12x+36+400=x^2+400+16-8\sqrt{x^2+400}\)
to get
\(2\sqrt{x^2+400}=3x-5\)
now squaring again:
\(4(x^2+400)=9x^2+25-30x\)
solving this u get,x=21. ok?

Answer 6

the other negative root x=-15 is ignored because the length cannot be negative.

Answer 7

yap.. thanks much:)

Answer 8

welcome :)