Question 1096569
The perimeter of a rectangular plot of land is 70 meters.
2L + 2w = 70
simplify, divide by 2
L + w = 35
L = -w + 35, we can use this form for substitution
:
 The length of a diagonal is 25 meters.
{{{L^2 + w^2 = 25^2}}}
{{{L^2 + w^2 = 625}}}
Replace L with (-w+35)
{{{(-w+35)^2 + w^2 = 625}}}
FOIL (-w+35)(-w+35)
{{{w^2 - 35w - 35w + 1225 + w^2 = 625}}}
arrange as a quadratic equation
{{{2w^2 - 70w + 1225 - 625 = 0}}}
{{{2w^2 - 70w + 600 = 0}}}
simplify divide by 2
{{{w^2 - 35w + 300 = 0}}}
You can use the quadratic formula; a=1;b=-35;c=300, but this will factor to:
(w-15)(w-20) = 0
two solution
w = 15 m is the width, then the length 35 - 15 = 20 m  
or
w = 20 m is the width, then the length is 15 m
:
 calculate the length and width of the plot: 20 by 15 
:
;
:
Check this solution by finding the diagonal
d = {{{sqrt(20^2 + 15^2)}}}