Quandaries and Queries


Who is asking: Other
Level: Secondary

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


M = 3x - 3 = x + 2

Solve for x.



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