Who is asking: Other
Level: Secondary
Question:
Hi - I have a measurement question that involves using the substitution
method for algebra. The answer is 2.5 but I don't know how the answer
was derived. The question is as follows:
The rectange has an area of M square units and a perimeter of 2M units. What is the value of x?
The length of the rectange is 3, while the width of the rectange is x-1.
Thank you.
Hi Sandy,
I drrew a diagram of a rectangle and indicated the lengths of the sides.
The area of a rectangle is the length times the width and hence the area of this rectangle is
3
(x-1) = 3x - 3
But the area is M so
3x - 3 = M
The perimeter of this rectangle is
3 + (x-1) + 3 + (x-1) = 6 + 2x -2 = 2x + 4
But the perimeter is 2M and hence
2x + 4 = 2M or x + 2 = M
Hence
M = 3x - 3 = x + 2
Solve for x.
Penny