document.write( "Question 648113: A farmer has 40 metres of fencing with which he intends to make a rectangular enclosure for a few sheep and their lambs. The farmer calculates that he requires 96m²of grass in the sheep pen. By forming a quadratic equation find the dimensions of the pen \n" ); document.write( "

Algebra.Com's Answer #406555 by stanbon(75887) $\"\"$ $\"About$

You can put this solution on YOUR website!
A farmer has 40 metres of fencing with which he intends to make a rectangular enclosure for a few sheep and their lambs. The farmer calculates that he requires 96m²of grass in the sheep pen. By forming a quadratic equation find the dimensions of the pen
\n" ); document.write( "-----
\n" ); document.write( "Perimeter = 2(L + W) = 40 metres
\n" ); document.write( "----
\n" ); document.write( "Area = L*W = 96 m^2
\n" ); document.write( "----
\n" ); document.write( "Solve the 1st equation for \"L\":
\n" ); document.write( "L + W = 20
\n" ); document.write( "L = 20-W
\n" ); document.write( "----
\n" ); document.write( "Sustitute into the 2nd equation and solve for \"W\":
\n" ); document.write( "(20-W)W = 96
\n" ); document.write( "20W-W^2 = 96
\n" ); document.write( "W^2 - 20W + 96 = 0
\n" ); document.write( "----
\n" ); document.write( "(W -16)(W-4) = 0
\n" ); document.write( "Width = 16 m or Width = 4 m
\n" ); document.write( "---
\n" ); document.write( "If W = 16, then L = 4
\n" ); document.write( "If W = 4, then L = 16
\n" ); document.write( "=========================
\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
\n" ); document.write( "========================= \n" ); document.write( "

\n" );