Question

If side of a scalene is tripled then area would be increased by​

Answer 1

Answer:

here it is your answer !!

Step-by-step explanation:

as we get area by Heron's formula,  

let the 3 sides be a,b and c  

so,

S= a+b+c/2  

BUT

now you have each side doubled so,  

S= (2a+2b+2c)/2

S= a+b+c

so, S has doubled.

so area = √{2S (2S-2a)(2S-2b)(2s-2c)}

=> √4{ S(S-a)(S-b)(S-c)}

=> 2 × area

Therefore, area doubles!

Answer 2

Answer:

kindly see the answer below...

Step-by-step explanation:

Here, let the real scalene triangles ΔABC, has side AB, BC, CA.

now, the side of the triangle is tripled so, newly formed scalene triangle is ΔPQR,

where, PQ=3AB ,QR=3BC ,RP=3CA.

therefore, the triangle ΔABC similar to ΔPQR.

then, according to the similarity rule,

$\frac{ar(abc)}{ar(pqr)} = \frac{ {(ab)}^{2} }{ {(pq)}^{2} }$

$= \frac{ {(ab)}^{2} }{ {(3ab)}^{2} }$

$= \frac{1}{9}$

so, the area of the newly formed triangle would be 9 times the area of the real scalene triangle.

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