Question

In the adjoining figure, all measurements are in centimetres. Find the Perimeter of the quadrilateral ABCD​

Answer 1

Answer:

perimeter of quadrilateral = 40cm

Step-by-step explanation:

$perimeter \: of \: triangle \: abc \\ ac {}^{2} = ab {}^{2} + bc {}^{2} \\ ac {}^{2} = 8 {}^{2} + 6 {}^{2} \\ ac {}^{2} = 64 + 36 \\ ac {}^{2} = 100 \\ ac = \sqrt{100} \\ ac = 10 \\ therefore \: ac \: is \: 10cm \\ \\ let \: \\ the \: centre \: point \: of \: diagonal \: be \: o \\ ad = dc \\ half \: of \: ac \:is \: 5cm \\ ad {}^{2} = ao {}^{2} + od {}^{2} \\ ad {}^{2} = 5 {}^{2} + 12 {}^{2} \\ ad {}^{2} = 25 + 144 \\ ad {}^{2} = 169 \\ ad = \sqrt{169} \\ ad = 13 \\ therefore \: ad \: = \: 13cm \\ ad = dc \\ so \: dc \: = 13cm \\ permimeter \: of \: quadilateral \\ = sum \: of \: its \: sides \\ = (8 + 6 + 13 + 13)cm \\ = 40cm$

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