C-16-Q027mediumsingle_mcq

If the perpendiculars from an interior point to the three sides of an equilateral triangle are $p_1, p_2, p_3$ , the side $a$ satisfies —

a $p_1 + p_2 + p_3 = \dfrac{\sqrt{3}}{2}a$
b $p_1 + p_2 + p_3 = a$
c $p_1 + p_2 + p_3 = \dfrac{a}{2}$
d $p_1 + p_2 + p_3 = \sqrt{3}\,a$

ব্যাখ্যা

The three perpendiculars split the triangle into three smaller triangles whose areas sum to the whole: $\frac{1}{2}a(p_1+p_2+p_3) = \frac{\sqrt{3}}{4}a^2$ . This simplifies to $p_1+p_2+p_3 = \frac{\sqrt{3}}{2}a$ (Viviani's theorem).

এই অধ্যায়ের আরও প্রশ্ন

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

If the perpendiculars from an interior point to the three sides of an equilateral triangle are $p_1, p_2, p_3$ , the side $a$ satisfies —

p_1 + p_2 + p_3 = \dfrac{\sqrt{3}}{2}a

p_1 + p_2 + p_3 = a

p_1 + p_2 + p_3 = \dfrac{a}{2}

p_1 + p_2 + p_3 = \sqrt{3}\,a

If the perpendiculars from an interior point to the three sides of an equilateral triangle are p1,p2,p3p_1, p_2, p_3p1​,p2​,p3​, the side aaa satisfies —

ব্যাখ্যা

এই অধ্যায়ের আরও প্রশ্ন

If the perpendiculars from an interior point to the three sides of an equilateral triangle are p1,p2,p3p_1, p_2, p_3p1​,p2​,p3​, the side aaa satisfies —

ব্যাখ্যা

এই অধ্যায়ের আরও প্রশ্ন

If the perpendiculars from an interior point to the three sides of an equilateral triangle are $p_1, p_2, p_3$ , the side $a$ satisfies —

If the perpendiculars from an interior point to the three sides of an equilateral triangle are $p_1, p_2, p_3$ , the side $a$ satisfies —