MHB What is the multiplier for finding the area of triangle ADG?

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SUMMARY

The discussion focuses on calculating the area of triangle ADG using the formula for the area of a triangle, \( A = \frac{bh}{2} \). The area of triangle CDE is expressed in terms of segments AG and DG, leading to the equation \( \frac{\frac{1}{3}AG \cdot \frac{1}{3}DG}{2} = 42 \). Participants explore the necessary multiplier to derive the area of triangle ADG from this equation. The conversation highlights the importance of understanding geometric relationships and area calculations in triangle geometry.

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  • Knowledge of geometric proportions and segment relationships
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  • Basic concepts of similar triangles and their properties
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  • Research the properties of similar triangles and their area ratios
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Not sure how to use a single area and line segments that are same to calculate the areas and line segments for the areas.
 

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Using the formula for the area, $A$, of a triangle

$$A=\frac{bh}{2}$$

where $b$ is the base of the triangle and $h$ is the height of the triangle, can you state the area of triangle $CDE$ in terms of $AG$ and $DG$?
 
(3)42 = 84/2 so b times h equals 84
 
$$\frac{\frac13AG\cdot\frac13DG}{2}=42$$

Now, what number can we multiply both sides of the above equation by to find $\triangle{ADG}$?
 
greg1313 said:
$$\frac{\frac13AG\cdot\frac13DG}{2}=42$$

Now, what number can we multiply both sides of the above equation by to find $\triangle{ADG}$?

Greg, I'm glad you can read that tiny sideways image, because I sure can't. (Bandit)
 

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