Question

*Ratio of corresponding sides of two similar triangles is 2ः5, If the area of the small triangle is 64 sq.cm. then what is the area of the bigger triangle ?* 1️⃣ 200 sq.cm. 2️⃣ 400 sq.cm. 3️⃣ 800 sq.cm. 4️⃣ 100 sq.cm.​

Answer 1

Answer:

Solution

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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

Step-by-step explanation:

Answer 2

Given:

The ratio of corresponding sides of two similar triangles is 2:5, If the area of the small triangle is 64 sq. cm. then what is the area of the bigger triangle?

To find:

The area of the bigger triangle

Solution:

Let's say the ratio is given as,

$\frac{Side\:of\:smaller \:tirangle}{Side\:of\:bigger\:triangle} = \frac{2}{5}$

So, we get

"2x" and "5x" are the corresponding sides of the smaller and bigger triangles respectively.

The area of the smaller triangle = 64 sq. cm

We know,

The ratio of the areas of two similar triangles will be equal to the square of the ratio of the corresponding sides of these triangles.

Therefore, from the above theorem, we get

$\frac{Area\:smaller\:\triangle}{Area\:bigger\:\triangle} = (\frac{Side\:of\:smaller \:tirangle}{Side\:of\:bigger\:triangle})^2$

$\implies \frac{64}{Area\:bigger\:\triangle} = (\frac{2x}{5x})^2$

$\implies \frac{64}{Area\:bigger\:\triangle} = \frac{4}{25}$

$\implies Area\:bigger\:\triangle = \frac{64 \times 25}{4}$

$\implies \bold{Area\:bigger\:\triangle = 400\:cm^2}$ ← option (2)

Thus, the area of the bigger triangle is → 400 sq. cm.

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