Question

triangle def similar triangle abc, if de:ab=2:3 and ar(tri.def) is equal to 44square units .find the area (tri. abc)

Answer 1

I thought that it will help you and please mark me as brainliest

Answer 2

The area of triangle ABC is 99 square units.

Step-by-step explanation:

Given:

Δ DEF ~ Δ ABC

$\dfrac{DE}{AB}=\dfrac{2}{3}$

Ar(ΔDEF) = 44 units²

To Find:

Ar(ΔABC) = ?

Solution:

Δ DEF ~ Δ ABC        ...............Given

If two triangles are similar then the ratios of the ideas of the triangles is equal to the ratio of the squares of corresponding sides.

$\dfrac{Ar(\triangle DFE )}{Ar(\triangle ACB )}= \dfrac{DE^{2}}{AB^{2}}$

Substituting the value we get

$\dfrac{44}{Ar(\triangle ABC )}= (\dfrac{2}{3})^{2} =\dfrac{4}{9} \\\\Ar(\triangle ABC)=\dfrac{9\times 44}{4}=9\times 11=99\ unit^{2}$

The area of triangle ABC is 99 squareunits.