Question

scarlet walks along the edges of a rectangular paths from A to B to C. to D a distance of 38 metres.Jake walks along the same rectangle but from B to C to D to A of only 31 m .What is the area in square metres of rectangle ABCD

Answer 1

2x+y = 38
x+2y = 31
x=15, y=8 so the area is 15*8 = 120

Answer 2

let AB = CD = y
let BC = DA = x
Scarlets distance : 2y + x = 38
Jake's distance : 2x + y = 31

double the first equation: 2x + 4y = 76
the 2nd equation as is: 2x + y = 31
subtract them ----> 3y = 45, y = 15
in 2y + x = 38, we get x = 8

area of rectangle = xy = 8*15 or 120 m^2

check my calculations.