C-16-Q028mediumsingle_mcq

If the three perpendiculars from an interior point of an equilateral triangle to the sides are $6, 7, 8$ cm, the length of a side is —

a $7\sqrt{3}$ cm
b $\dfrac{14}{\sqrt{3}}$ cm
c $14\sqrt{3}$ cm
d $21\sqrt{3}$ cm

ব্যাখ্যা

By Viviani's theorem, $p_1+p_2+p_3 = \frac{\sqrt{3}}{2}a$ , so $6+7+8 = 21 = \frac{\sqrt{3}}{2}a$ . Solving gives $a = \frac{42}{\sqrt{3}} = 14\sqrt{3}$ cm.

এই অধ্যায়ের আরও প্রশ্ন

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Chapter 16: Mensuration — সব প্রশ্ন দেখুন (210টি) →

If the three perpendiculars from an interior point of an equilateral triangle to the sides are $6, 7, 8$ cm, the length of a side is —

7\sqrt{3}

\dfrac{14}{\sqrt{3}}

14\sqrt{3}

21\sqrt{3}

ব্যাখ্যা

By Viviani's theorem, $p_1+p_2+p_3 = \frac{\sqrt{3}}{2}a$ , so $6+7+8 = 21 = \frac{\sqrt{3}}{2}a$ . Solving gives $a = \frac{42}{\sqrt{3}} = 14\sqrt{3}$ cm.

If the three perpendiculars from an interior point of an equilateral triangle to the sides are 6,7,86, 7, 86,7,8 cm, the length of a side is —

ব্যাখ্যা

এই অধ্যায়ের আরও প্রশ্ন

If the three perpendiculars from an interior point of an equilateral triangle to the sides are 6,7,86, 7, 86,7,8 cm, the length of a side is —

ব্যাখ্যা

এই অধ্যায়ের আরও প্রশ্ন

If the three perpendiculars from an interior point of an equilateral triangle to the sides are $6, 7, 8$ cm, the length of a side is —

If the three perpendiculars from an interior point of an equilateral triangle to the sides are $6, 7, 8$ cm, the length of a side is —