Question

∆ABC ~ ∆DEF,If BC=4 cm, EF=5 cm and area of ∆ABC is 32 cm²,then the area of ∆DEF is
PLZ HELP

Answer 1

Answer:

$\boxed{\red{\sf\:A\:(\:\triangle\:D EF\:)\:=\:50\:cm^2}}$

Step-by-step-explanation:

We have given that,

$\bullet\sf\:\triangle\:ABC\:\sim\:\triangle\:D EF\\\\\\\bullet\sf\:BC\:=\:4\:cm\\\\\\\bullet\sf\:EF\:=\:5\:cm\\\\\\\bullet\sf\:A\:(\:\triangle\:ABC\:)\:=\:32\:cm^2$

We have to find $\sf\:A\:(\:\triangle\:D EF\:)$

We know that,

Ratio of areas of two similar triangles is equal to the ratio of the squares of the corresponding sides.

$\pink{\sf\:\dfrac{\:A\:(\:\triangle\:ABC\:)}{\:A\:(\:\triangle\:D EF\:)}\:=\:\dfrac{(\:BC\:)^2}{(\:EF\:)^2}}\\\\\\\implies\sf\:\dfrac{32}{\:A\:(\:\triangle\:D EF\:)}\:=\:\dfrac{(\:4\:)^2}{(\:5\:)^2}\\\\\\\implies\sf\:\dfrac{32}{\:A\:(\:\triangle\:D EF\:)}\:=\:\dfrac{16}{25}\\\\\\\implies\sf\:16\:\times\:A\:(\:\triangle\:D EF\:)\:=\:32\:\times\:25\\\\\\\implies\sf\:A\:(\:\triangle\:D EF\:)\:=\:\dfrac{\cancel{32}\:\times\:25}{\cancel{16}}\\\\\\\implies\sf\:A\:(\:\triangle\:D EF\:)\:=\:2\:\times\:25\\\\\\\implies\boxed{\red{\sf\:A\:(\:\triangle\:D EF\:)\:=\:50\:cm^2}}$

Additional Information:

1. Similarity:

When two things are same in the view, then they are similar.

The best example of similarity is we and our photo. Both are same in view, but different in measurements.

2. Similarity in triangles:

In two triangles, when corresponding angles are congruent and corresponding sides are in proportion, the two triangles are known as similar.

3. Ratio of area of two triangles:

When two triangles are similar, the ratio of their area is equal to the ratio of squares of the corresponding sides.

4. Difference between Congryency & Similarity:

Congryency means two objects are totally equal, it may be view, or it may be measurement.

Similarity means two objects are only same in view and there measurements may be unequal.

Answer 2

GIVEN:

• ∆ABC ~ ∆DEF

• BC=4 cm

• EF=5 cm

• A(∆ABC)=32 cm²

TO FIND:

A(∆DEF)=?

SOLUTION:

Since,

We know that,

✨RATIO OF AREAS OF TWO TRIANGLES IS EQUAL TO THE RATIO OF THE SQUARES OF THEIR CORRESPONDING SIDES. ✨

A(∆ABC)/A(∆DEF)= (BC) ²/(EF) ²

→ 32/A(∆DEF)=(4)²/(5)²

→ 32/A(∆DEF)=16/25

→ A(∆DEF)×16=32×25

→ A(∆DEF)=32×25/16

→ A(∆DEF)= 50 cm².

Therefore Area of ∆DEF is 50 cm².