The perimeter of a rectangle is 56 m. if the width were doubled and the length were increased by 8 m, then the perimeter would be 82 m. what are the dimensions

Define x and y:

Let the length be x.
Let the width be y.


Formula:

Perimeter = 2(Length + Width)


Construct equations and solve for x and y:

2x + 2y = 56            (1)
2(x+8) + 4y = 82     (2)


From equation 1:

2x + 2y = 56
x + y = 28
x = 28 - y


From equation 2:

2(x+8) + 4y = 82 
2x + 16 + 4y = 82
2x + 4y = 66
x + 2y = 33


Substitute x = 28 - y into equation 2:

x + 2y = 33
(28 - y) + 2y = 33
28 - y + 2y = 33
y = 5


Substitute y = 5 into equation 1:

x = 28 - y 
x = 28 - 5
x = 23


Find Length and Width

Length = x = 23 m
Width = y = 5m


Length = 23m and Width = 5m

Recall that area of the triangle is 1/2*(base)*(height)1/2*(13)*(17) = 110.5the answer is 110.5