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
2x+y = 38
x+2y = 31
x=15, y=8 so the area is 15*8 = 120
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.
To find the area of the rectangle ABCD, we need to know the lengths of its sides. Let's call the length of the rectangle AB as 'a' and the width BC as 'b'.
We know that Scarlet walks along the edges of the rectangle from A to B to C to D, covering a distance of 38 meters. This can be expressed as:
AB + BC + CD + DA = 38
Similarly, Jake walks along the same edges, but in the opposite direction, from B to C to D to A, covering a distance of 31 meters:
BC + CD + DA + AB = 31
From these two equations, we can form a system of linear equations:
AB + BC + CD + DA = 38 (Equation 1)
BC + CD + DA + AB = 31 (Equation 2)
To simplify the equations, we observe that the distances along the sides of the rectangle are equal. So, we can rewrite the equations as:
2AB + 2BC = 38 (Equation 3)
2BC + 2CD = 31 (Equation 4)
Rearranging Equation 3, we have:
AB + BC = 19 (Equation 5)
Substituting Equation 5 into Equation 4, we can solve for BC:
2(AB + BC) + 2CD = 31
2(19) + 2CD = 31
38 + 2CD = 31
2CD = 31 - 38
2CD = -7
CD = -7/2 or -3.5
Since lengths cannot be negative, we discard the negative value.
Now that we have the values of AB, BC, and CD, we can calculate the area of the rectangle. The area of a rectangle is given by the formula:
Area = Length × Width
Area = AB × BC
Plugging in the values of AB = 19 and BC = 19 - AB into the equation, we get:
Area = 19 × (19 - 19)
Area = 19 × 0
Area = 0
Therefore, the area of the rectangle ABCD is 0 square meters.