Question

Triangle DEF is congruent to triangle ABC,If DE:AB =2:3and area of triangle FED is equal to 44 square units. Find the area of triangle ABC.

Answer 1

So the answer will be 99 square unit the area of triangle ABC

Answer 2

Note: Triangle DEF is similar to triangle ABC

Find the area of triangle ABC:

$\dfrac{\text {Area of }\triangle \text {1} }{\text {Area of }\triangle \text {2} } = \bigg( \dfrac{\text {Length of }\triangle \text {1} }{\text {Length of }\triangle \text {2}}\bigg)^2$

$\dfrac{\text {44} }{\text {Area of }\triangle \text {2}} = \bigg( \dfrac{2}{3} \bigg)^2$

$\dfrac{\text {44} }{\text {Area of }\triangle \text {2}} = \dfrac{4}{9}$

$4 \times \text {Area of }\triangle \text {2} = 9 \times 44$

$4 \times \text {Area of }\triangle \text {2} = 396$

$\text {Area of }\triangle \text {2} = 396 \div 4$

$\text {Area of }\triangle \text {2} = 99 \text{ m}^2$

Answer: The area is 99 m²