The sides of a triangle are 28 cm, 45 cm, and 53 cm. What is its area? (in cm2 )
The sides of a triangle are 28 cm, 45 cm, and 53 cm. What is its area? (in cm$^2$ )
एक त्रिभुज की भुजाएँ 28 सेमी, 45 सेमी और 53 सेमी हैं। इसका क्षेत्रफल (सेमी² में) ज्ञात कीजिए।
Detailed Solution & Logic
Correct Answer:
630
दिए गए त्रिभुज की भुजाएँ: 28 सेमी, 45 सेमी, 53 सेमी
अर्द्धपरिमाप (semi-perimeter):
$s = \frac{28 + 45 + 53}{2} = \frac{126}{2} = 63$
अब, हेरॉन सूत्र:
क्षेत्रफल $= \sqrt{s(s-a)(s-b)(s-c)}$
$= \sqrt{63(63-28)(63-45)(63-53)}$
$= \sqrt{63 \times 35 \times 18 \times 10}$
अब गणना:
$63 \times 35 \times 18 \times 10 = 396900$
$= \sqrt{396900} = 630$
सही उत्तर: 630 सेमी²
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