Question : What is the area of a triangular flower bed of a garden whose perimeter is 20 m and two sides are 5 m and 6 m?
Option 1: $10 \sqrt{2}$ m2
Option 2: $2 \sqrt{10}$ m2
Option 3: $5 \sqrt{2}$ m2
Option 4: $4 \sqrt{5}$ m2
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Correct Answer: $10 \sqrt{2}$ m 2
Solution :
Perimeter = 20 m
Two sides are 5 m and 6 m.
Third side = 20 – 5 – 6 = 9 m
Semi perimeter, $ s = \frac{a+b+c}{2} = \frac{20}{2} = 10$
Area of triangle $= \sqrt{s(s-a)(s-b)(s-c)}$
$= \sqrt{10(10-5)(10-6)(10-9)}$
$= \sqrt{10×5×4}$
$=\sqrt{200}$
$=10 \sqrt{2}$ m
2
Hence, the correct answer is $10 \sqrt{2}$ m
2
.
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