Question

Find the dimensions of a rectangular persian rug whose perimeter is 18 ft and whose area is 20 ft squared.the persian rug has a length? (longer side) of nothing ft and a width? (shorter side) of nothing ft.

Answer 1

Hello : 
 x : the  length  and y the width    ....x > y
2(x+y) = 18 ...(1)
xy = 20...(2)
by (1) : x +y = 9
y = 9 - x 
subcste in (2)
x( 9 - x ) = 20
-x² +9x = 20
  x² -9x +20 = 0 
(x-4)(x-5) = 0
x-4=0 or x -5 =0 
 x=4 or x= 5
if : x = 4     y = 9-4 =5 ....refused because : x > y
if : x= 5    y = 9-5 = 4
conclusion : 
he  length is : 5 feet  and the width  is : 4 feet