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Home Continuous Functions How to Set Up a Problem Examples Example 5
 
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Example 5

The area of square A is twelve square units greater than the area of square B, and the side of A is three units greater than the side of B. Find the areas of A and B.

03_continuous_functions-12.gif

Figure 3.1.5

Step 1

Let a be the area of A and b the area of B. See Figure 3.1.5.

Step 2

The sides of the squares have length √a and √b respectively. Thus

a - b = 12, √a - √b = 3.

Step 3

We find √a + √b.

(√a - √b)(√a + √b) = a - b,

3(√a + √b)= 12,

√a + √b = 4.

Adding the equations √a + √b = 4 and √a - √b = 3, we obtain

2√a = 7, √a = 7/2, a = 49/4.

Subtracting the equations gives

2√b = 1,

√b = ½, b = ¼

INTERPRET THE SOLUTION

The area of square A is 49/4 square units, and the area of square B is ¼ square units.
Home Continuous Functions How to Set Up a Problem Examples Example 5

Last Update: 2006-11-15