Question

ΔDEF ~ ΔABC,if DE : AB = 2:3 and ar (ΔDEF)is equal to 44 square units. Find the area(ΔABC).

Answer 1

your answer............................

Answer 2

Answer:

Concept:

Finding the area of a triangle by using the area of a similar triangle.

Ratio of area of similar triangles in equal to the ratio of square of its corresponding side.

Step-by-step explanation:

Given:
$\triangle \mathrm{DE F} \sim \triangle \mathrm{ABC}$

$\mathrm{DE}: \mathrm{AB}=2: 3$

Find:

The area of (ΔABC).

Solution:

We know that,

Ratio of area of similar triangles in equal to the ratio of square of its corresponding side

   Therefore,    ar(ΔDEF) / ar((ΔABC)  $=\frac{(\mathrm{DE})^{2}}{(\mathrm{AB})^{2}}$

                                     44 / ar(ΔABC)   $=\left(\frac{2}{3}\right)^{2}$

                                             ar(ΔABC)   $=\frac{44 \times 9}{4}$

                                            ∴  ar(ΔABC) = $99cm^{2}$

The area  (ΔABC) is $99cm^{2}$.

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