Question

prove that the ratio of the areas two similar triangle is equal to the squre of the ratio of their corresponding sides. (plz answer it fast plz) ​

Answer 1

Step-by-step explanation:

Let the two triangles be:

ΔABC and ΔPQR

Area of ΔABC= 1/2  ×BC×AM……………..(1)

Area of ΔPQR=1/2  ×QR×PN……………………..(2)

Dividing (1) by (2)

ar(ABC)/ar(PQR)  =1/2×BC×AM/1/2×QR×PN

ar(ABC)/ar(PQR) =BC×AM/QR×PN…………………..(1)

In ΔABM and ΔPQN

∠B=∠Q (Angles of similar triangles)

∠M=∠N (Both 90∘  )

Therefore, ΔABM∼ΔPQN

So,  

AB/AM=PQ/PN …………………….(2)

From 1 and 2

ar(ABC)/ar(PQR)=BC/QR ×AM/  PN

⇒  ar(ABC)/ar(PQR)=BC/QR ×AB/PQ …………………..(3)

AB/PQ  =BC/QR  =  AC/PR………….(ΔABC∼ΔPQR)  

Putting in ( 3 )  ar(ABC)  / ar(PQR)  =AB/PQ  ×AB/PQ =( AB/PQ )2

⇒  ar(ABC)/ar(PQR) =(  AB/PQ  )2  =(  BC/QR  )  2 =(  AC/PR )  2

here is your answer dear!!!