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guapka [62]
3 years ago
9

In ABC, D∈AB so that AD;DB=1 : 3. If ACDB = 12ft2 Find AACD and AABC

Mathematics
1 answer:
Sergeeva-Olga [200]3 years ago
3 0

Answer:

Area of \triangleACD = 4 ft^2

Area of \triangleABC = 16 ft^2

Step-by-step explanation:

Given that:

D is a point on AB.

and ABC is a triangle.

AD:DB = 1 : 3

Area of \triangleCDB = 12 ft^2

Kindly refer to the attached image as per the given dimensions and values.

To find:

Area of \triangleACD and Area of \triangleABC = ?

Solution:

Formula for area of a triangle = \frac{1}{2}\times Base \times Height

The altitudes of triangles \triangleCDB and \triangleACD are equal in dimensions.

Therefore the area of triangles \triangleCDB and \triangleACD will be equal to the ratio of their bases.

Area of \triangleACD : Area of \triangleCDB = AD: DB = 1 : 3

\Rightarrow Area of \triangleACD = \frac{12}{3} = \bold{4 ft^2}

Area of \triangleABC = Area of \triangleACD + Area of \triangleCDB = 12 + 4 = <em>16</em> ft^2

Therefore, the answer is:

Area of \triangleACD = 4 ft^2

Area of \triangleABC = 16 ft^2

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