Question

in the given figure DE is parallel to BC if BC=8 cm and DE=6 cm and area of triangle ABC is equal to 45 CM square find the area of triangle ABC

Answer 1

Hope it helps ..................

Answer 2

The area of triangle ABC is 80cm².

In the given figure DE is parallel to BC if BC = 8cm and DE = 6cm and area of triangle ADE is 45cm².

We have to find the area of triangle ABC.

Let's draw the diagram as they said. see attached figure, here it is clear that

$\Delta ADE\sim\Delta ABC$

We know,

"If two triangles are similar, then the ratio of area of both triangles is proportional to the square of the ratio of their corresponding sides."

$\frac{\Delta ADE}{\Delta ABC}=\frac{DE^2}{BC^2}$

Here, ΔADE = 45 cm², DE = 6cm, and BC = 8 cm

⇒ 45cm²/ΔABC = 6²/8² = 36/64 = 9/16

⇒ ΔABC = 80 cm²

Therefore the area of triangle ABC is 80cm².

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