How to do the question in the image below?

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Answer 1 · 2018-02-28T05:50:25

(a) #color(green)(Perimeter of triangle PQR = a + a + a = 3a#

(b) #color(purple)(Area of Delta PQR = (sqrt3 / 4) a^2#

P,Q,R are the midpoints of sides AB,BC,CA of equilateral triangle ABC.

# AB = BC = CA#

Consider triangles # ABC, PQR#

#AP = PB = (AB)/ 2#

#AQ = QC = (AC) / 2 #

#hat A # common for both triangles.

Hence #Delta ABC, PQR# are similar and #Delta PQR# is also an equilateral triangle.

#:. PQ = QR = RP = (AB) / 2 = (2a) / 2 = a#

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(a) #color(green)(Perimeter of triangle PQR = a + a + a = 3a#

(b) #color(purple)(Area of Delta PQR = (sqrt3 / 4) a^2#