Question

a pond of rectangular shape is constructed with perimeter 42 meter and diagonal length 15 centimeter if breadth of pond is x what is its length from a second degree equation and hence find length and breadth of the pond​

Answer 1

$\bold\blue{Question}$

A pond of rectangular shape is constructed with perimeter 42 meter and diagonal length 15 meter if breadth of pond is x what is its length from a second degree equation and hence, find length and breadth of the pond.

$\bold\red{\underline{\underline{Answer:}}}$

$\bold\purple{Explanation}$

To get length and breadth we must form the equations and solve them.

$\bold\orange{Given:}$

$\bold{Breadth=x \ cm...given}$

$\bold{Perimeter=42 m}$

$\bold{Diagnoal=15m}$

$\bold\pink{To \ find:}$

Length(l) and breadth(b) of the rectangle.

$\bold\green{\underline{\underline{Solution}}}$

Perimeter=2(l+b)

42=2(l+x)

Divide both sides by 2,we get

l+x=21

l=21-x

Now length(l) is (21-x)m and breadth is x m,

Length, breadth and diagonal forms a right angled triangle.

By Pythagoras theorem,

$\bold{15^{2}=(21-x)^{2}+x^{2}}$

$\bold{225=441-42x+x^{2}+x^{2}}$

$\bold{2x^{2}-42x+441-225=0}$

$\bold{2x^{2}-42x+216=0}$

Divide both sides by 2,we get

$\bold{x^{2}-21x+106}$

$\bold{Here,a=1,b=-21,c=106}$

By formula method

$\bold{x=\frac{-b+\sqrt(b^{2}-4ac)}{2a} \ or \frac{-b-\sqrt(b^{2}-4ac)}{2a}}$

$\bold{x=\frac{21+\sqrt17}{2} or \frac{21-\sqrt17}{2}}$

Length=21-x

Length=21-$\bold{(\frac{21+\sqrt17}{2} or \frac{21-\sqrt17}{2})}$

Length=$\bold{\frac{21+\sqrt17}{2} \ or \frac{21+\sqrt17}{2}}$