Question

23.
There is a triangular park in the society. The residents of society decided
to divide the park into two parts by constructing walls from mid point of
any two sides of a park resulting in formation of a smaller triangular park
and a quadrilateral park. If the perimeter of original park is 35 m. Find the
perimeter of small triangular park formed.

PLEASE ANSWER THIS QUESTION.​

Answer 1

GIven : A triangular park in the society , park divided into two parts by constructing walls from mid point of any two sides of a park

To find : perimeter of small triangular park formed.

Solution:

Let say Triangular Park PQR

Given Perimeter of original Park = 35 m

=> PQ + QR + PR = 35

Now let say mid point of   PR (D) & QR   (E)   are joined

to form  a smaller triangular park RDE

and a quadrilateral park.  PQED

RD = PR/2   &  RE = QR/2   ( as mid point)

=> RD/PR = RE/QR  = 1/2

& ∠R common

ΔRDE ≈ ΔRPQ

=> RD/RP  = RE/QR  = DE/PQ   = 1/2

=> RD = PR/2

   RE = QR/2

   DE = PQ/2

Perimeter of smaller triangle RDE

RD + DE + RE

= ( PR/2 + PQ/2 + QR/2)

= (PR + PQ + QR)/2

= 35/2

= 17.5 cm

the perimeter of small triangular park formed =  17.5 cm

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