Question

if triangle ABC similar to triangle DEF, BC=4cm, EF=5cm and area of triangle ABC=80cm^2 find area of traingle DEF

Answer 1

ar(ABC)/ar(DEF)=BC/EF. (by theorem)

80/ar(DEF)=4/5

ar(DEF)=80*5/4

ar(DEF)=100 cm sq.

Answer 2

Answer:

$Area\: \triangle DEF=125 \: cm^{2}$

Step-by-step explanation:

Given , ∆ABC ~∆DEF,

BC=4 cm, EF=5 cm ,

Area of ∆ABC = 80 cm²,

Area of ∆DEF = ?

/* we know the Theorem:

The ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides. */

$\frac{Area\: \triangle ABC}{Area\: \triangle DEF}=\frac{BC^{2}}{EF^{2}}$

$\implies \frac{80}{Area\: \triangle DEF}=\frac{4^{2}}{5^{2}}$

$\implies \frac{80}{Area\: \triangle DEF}=\frac{16}{25}$

$\implies Area\: \triangle DEF=\frac{25}{16}\times 80 \\=125 \: cm^{2}$

Therefore,

$Area\: \triangle DEF=125 \: cm^{2}$

••••♪