Question

In A ABC, DE || AB, AD = 3DC, A(OABED)=90 cm?.
Find A (AABC)​

Answer 1

Given:

In A ABC, DE || AB, AD = 3DC, A(OABED)=90 cm?

To Find:

Find A (AABC)​

Step-by-step explanation:

• In ΔABC using Basic proportionality theorem we can write $DC\div DE=AC\div AB\\=(AD+DC)\div AB\\=4DC\div AB\\AB=4DE$
• As ΔABC  is congurent to ΔDEC

$Area(ABED)\div Area(ABC)=((AB)^{2} -(DE)^{2})\div (AB)^{2}\\= 15\times (DE)x^{2} \div 16\times (DE)x^{2} \\=15\div 16\\area(ABC)=(90\times 16)\div 15=96\ cm^{2}$

The final answer is 96 $cm^{2}$

Answer 2

Answer:

Given:

In A ABC, DE || AB, AD = 3DC, A(OABED)=90 cm?

To Find:

Find A (AABC)

Step-by-step explanation:

In ΔABC using Basic proportionality theorem we can write \begin{gathered}DC\div DE=AC\div AB\\=(AD+DC)\div AB\\=4DC\div AB\\AB=4DE\end{gathered}

DC÷DE=AC÷AB

=(AD+DC)÷AB

=4DC÷AB

AB=4DE

As ΔABC is congurent to ΔDEC

\begin{gathered}Area(ABED)\div Area(ABC)=((AB)^{2} -(DE)^{2})\div (AB)^{2}\\= 15\times (DE)x^{2} \div 16\times (DE)x^{2} \\=15\div 16\\area(ABC)=(90\times 16)\div 15=96\ cm^{2}\end{gathered}

Area(ABED)÷Area(ABC)=((AB)

2

−(DE)

2

)÷(AB)

2

=15×(DE)x

2

÷16×(DE)x

2

=15÷16

area(ABC)=(90×16)÷15=96 cm

2

The final answer is 96 cm^{2}cm

2