Question

ratio of corresponding sides of two triangles is 2:5, if the area of the smaller triangle is 64 sq.cm then what is the area of the bigger triangle

Answer 1

Answer:

MATHS

Ratio of corresponding sides of two similar triangles is 2:5,if the area of the smaller triangle is 64sq cm,then what is the area of the bigger triangle?

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ANSWER

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 .

Here ,

Let A

1

,A

2

are areas of two similar

triangles and s

1

,s

2

are their

corresponding sides respectively ,

s

1

:s

2

=2:5

=>s

1

/s

2

=2/5 -----(1)

A

1

=64m²,

A

2

=?

(s

1

/s

2

)²=(A

1

/A

2

)

=>(2/5)²=(64/A

2

)

=>A

2

=(64×25)/4

=16×25

=400

Therefore ,

Area of bigger triangle (A

2

)=400cm²

Answer 2

Given :-

Ratio of corresponding sides of two triangles = 2 : 5

Area of the smaller triangle = 64 cm²

To Find :-

Area of the bigger triangle.

Analysis :-

Ratio of the area is to ratio of the length.

Consider the area of the bigger triangle as a variable.

Substitute their values accordingly.

Then you can easily find the value of the variable.

Solution :-

Let the area of bigger triangle be 'x'.

According to the question,

$\sf \dfrac{Area \ 1}{Area \ 2} = \bigg( \dfrac{Length \ 1}{Length \ 2} \bigg)^2$

Given that,

Ratio = 2 : 5

Area of 1 = 64 cm²

Substituting their values,

64/x = (2/5)²

64/x = (4/25)

By transposing,

x = (64 × 24) ÷ 4

x = 1600 ÷ 4

x = 400 cm²

Therefore, the area of the bigger triangle is 400 cm².