Chocolate is in the form of a quadrilateral with sides 6cm and 10cm,5cm and 5cm(as shown in the figure)is
cut into two parts on one of its diagonal by a lady. Part-I is given to her maid and Part-II is equally divided
among a driver and Gardner.
ii. Area of ∆ABD
a)24cm2
b) 12cm2
c) 42cm2
d) 21cm2
Answers
Answer:
ans is c
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Answer:
There is a figure that goes with this question. The figure is attached.
ΔABD is a right angled triangle
∴ AB² + BD² = AD²
or BD² = AD² - AB²
or BD² = 10² - 6²
or BD² = 100 - 36
or BD² = 64
or BD = 8
Area of ΔABD = 1/2 × 6 × 8 = 24 cm²
Area of ΔBCD can be calculated using Heron's formula
Area = \sqrt{s(s-a)(s-b)(s-c)}
s(s−a)(s−b)(s−c).
semi-parameter s = (5+5+8)/2 = 9
Area = \sqrt{9(9-8)(9-5)(9-5)}
9(9−8)(9−5)(9−5)
= \sqrt{9(4)(4)}
9(4)(4)
= 12 cm²
ΔBCD forms Part-I and ΔABD forms Part-II
Part-2 is equally divided between driver and gardener so they both get the chocolate of area 12 cm²
Thus the distribution is fair
The lady has distributed the chocolate among the three indiscriminately. This shows that she cares for all three and there is no biased.