Which of the following can be the sides of a right triangle? 5m,6m,8m 7m,9m,11m 10m.25m,32m 9m,12m,15m
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Answer:
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Step-by-step explanation:
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Class 9
>>Maths
>>Heron's Formula
>>Area of Quadrilateral
>>Find the area of a quadrila...
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Find the area of a quadrilateral whose sides are 12,5,6 and 15. The angle between the first two sides is 90. (Use Heron's formula)
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Solution
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Correct option is
C
30+ 2
374
Consider ABCD is a quadrilateral where,
AB=12,BC=5,CD=6,DA=15 and ∠ABC=90
o
Area of ABCD= Area of ΔABC+Area of ΔACD
In Δ ABC, ∠B=90
o
Apply Pythagoras theorem in ΔABC
Therefore, AC
2
=AB
2
+BC
2
=12
2
+5
2
So, AC=13
Area of ΔABC=
2
1
×AB×BC=
2
1
×12×5=30m
2
In ΔACD, let s be the semiperimeter,
S=
2
6+15+13
=17m
Applying Heron's formula,
Area of ΔACD =
S(S−a)(S−b)(S−c)
=
17(17−13)(17−15)(17−6)
=
17(4)(2)(11)
=2
374
Hence, Area of quadrilateral ABCD=30+2
374
So, option C is correct.