Answer:
see the explanation
Step-by-step explanation:
Let
D -----> Danielle's age
C -----> Counselor's age
we know that
----> equation A
----> equation B
substitute
equation A in equation B
----> equation that can be used to find Danielle's age
Solve for D
<em>Find the value of C</em>
----> equation that can be used to find Counselor's age
substitute the value of D
therefore
Danielle's age is 7 and Counselor's age is 21
Check out the attached images below. In figure 1, I plotted the four points given as A, B, C, D; then connected them to form a rectangle.
Figure 2 shows 4 more points E, F, G, H made so that a larger rectangle forms. This newer larger rectangle entirely encloses the first rectangle. The idea is to find the area of the larger rectangle, and subtract off the areas of the four triangular pieces shown in figure 3. These images are attached below.
area of rectangle EFGH = base*height = 10*10 = 100
area of triangle ABE = base*height/2 = 3*3/2 = 4.5
area of triangle ADH = base*height/2 = 7*7/2 = 24.5
area of triangle CGD = base*height/2 = 3*3/2 = 4.5
area of triangle FCB = base*height/2 = 7*7/2 = 24.5
the four triangles have areas that add up to 4.5+24.5+4.5+24.5 = 58
Subtract this from the area of rectangle EFGH to get 100-58 = 42
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alternatively, you can find the distance from A to B getting roughly 4.24264 (use the distance formula). The distance from B to C is roughly 9.89949
Multiply those two values: 4.24264 * 9.89949 = 41.9999722536 which rounds to 42. There's rounding error based on the fact that the previously mentioned decimal values are approximate.
