Given: perimeter of triangle AQR = 15cm, perimeter of rectangle AQRF = 18cm. Find AR side.

In a rectangle, the opposite sides are equal to each other, which means AQ = RF and QR = AF, therefore the sum of the lengths of two adjacent sides of the rectangle is equal to half of the perimeter:

AQ + QR = RF + AF = PAQRF / 2 = 18/2 = 9 cm.

Knowing that the perimeter of the triangle AQR is 15 cm and AQ + QR = 9 cm, we find the side AR:

PAQR = AQ + QR + AR;

AR = PAQR – AQ – QR = PAQR – (AQ + QR) = 15 – 9 = 6 cm.