Question

if triangle ABC is congruent to DEF and AB=3DE with ar(triangle ABC)=144 sq cm, find ar(DEF)

Answer 1

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Answer 2

Answer:

$\text{The area of triangle DFE is }16 cm^2$

Step-by-step explanation:

Given if triangle ABC is congruent to DEF and AB=3DE with ar(ΔABC)=144 sq cm,

we have to find area of ΔDEF

As AB=3DE

⇒ $\frac{AB}{DE}=3$

As given the triangles are congruent i.e these are similar therefore the ratio of area of area of triangle is equal to the ratio of the square of their corresponding sides.

$\frac{ar(ABC)}{ar(DFE)}=(\frac{AB}{DE})^2$

$\frac{144}{ar(DFE)}=3^2$

$ar(DFE)=\frac{144}{9}=16 cm^2$