# 9.6.3. Solving Two Equations in Two Variables, One Is of the First Degree, and the Other Is of the Second Degree

The difference between the perimeters of two square-shaped pieces of land is 12 metres and that between their areas is 45 square metres. Find the side length of each of them.

• A6 metres, 9 metres
• B9 metres, 12 metres
• C12 metres, 15 metres
• D18 metres, 21 metres

### Example

The difference between the perimeters of two square-shaped pieces of land is 12 metres and that between their areas is 45 square metres. Find the side length of each of them.

### Solution

Denote the side length of the smaller square by and the side length of the larger square by .

If the difference between the perimeters of the two pieces of land is 12 metres, then which simplifies to

If the difference between the areas is 45 square metres, then

This pair of equations can be solved using the substitution method. Rearranging the first order equation gives

Substituting into the second order equation gives

Now substitute this value of into the first order equation to find .

Therefore, the side lengths of the two pieces of land are 6 metres and 9 metres.

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