Question

In △ABC, point D ∈ AB with AD:DB=5:3, point E ∈ BC so that BE:EC=1:4. If

Area of △ABC=40in², find the areas of △ADC, △BDC, and △CDE.

Answer 1

The areas of △ADC, △BDC, and △CDE within △ABC can be found by applying the given ratios to the total area of 40 in², using proportional reasoning specific to each sub-triangle.

Step-by-step explanation:

The question presented involves using ratios to find the areas of triangles within a larger triangle whose overall area is known. Given that △ABC has an area of 40in², point D divides AB in a 5:3 ratio, and point E divides BC in a 1:4 ratio, we need to find the areas of △ADC, △BDC, and △CDE.

To find the areas of the sub-triangles, consider the following steps:

1. Determine the ratio in which point D divides △ABC into smaller triangles △ADC and △BDC.
2. Similarly, calculate the ratio in which point E divides △ABC.
3. Apply the respective ratios to the original area of △ABC to find the areas of the resulting sub-triangles.

For instance, using the ratio of AD:DB, the area of △ADC would be 5/8 of the total area because the total parts when adding 5 and 3 is 8.

Thus, Area of △ADC = (5/8) * 40in². Following the same approach, the areas of the other triangles can be found accordingly, taking into account that △ADC and △BDC together make up △ABC, and △CDE is a part of △BDC subdivided by the ratio on side BC.