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Standard IX

Mathematics

Properties of Isosceles Triangle

In the adjace...

Question

In the adjacent figure 'P' is any interior point of the equilateral triangle ABC of side length 2 units.

If x_{a ,}x_b and x_c represent the distance of P from the sides BC, CA and AB respectively, then x_a + x_b + x_c is equal to

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√3

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√3/2

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2/√3

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Solution

The correct option is B
√3

Let A₁, B₁, C₁ are the foot of altitudes drawn from 'P' to sides BC, CA and AB respectively. We have,

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Similar questions

Q. In the adjacent figure

P

is any interior point of the equilateral triangle

A B C

of side length

2

units. If

x_{a}, x_{b}

and

x_{c}

represent the distance of

P

from the sides

B C, C A

and

A B

respectively then

x_{a} + x_{b} + x_{c}

is equal to

Q. In the adjacent figure P is any inferior point of the equilateral triangle ABC side length of

2

units. If

x_{a}, x_{b}

and

x_{c}

represent the distance of P from the sides BC,CA and AB respectively then

x_{a} + x_{b} + x_{c}

is equal to

Q. Let

^{'} P^{'}

is any arbitrary interior point of the triangle

A B C . H_{a}, H_{b}

and

H_{c}

are the length of altitudes drawn from the vertices

A, B

and

C

respectively.If

x_{a}, x_{b}

and

x_{c}

represent the distance of

^{'} P^{'}

from sides

B C, C A

and

A B

respectively, then the minimum value of

191 (\frac{H_{a}}{x_{a}} + \frac{H_{b}}{x_{b}} + \frac{H_{c}}{x_{c}})

must be

Q. A container is placed on a table has four holes. The

X_{A}, X_{B}, X_{C}

and

X_{D}

represent the horizontal distances covered by the liquid coming out from the holes

A, B, C,

and

D

respectively. Which of the following options is correct?

$In the adjacent figure, 'P' is any arbitrary interior of the triangle ABC,$ H_a, H_b, H_c $are the length of altitudes drawn from vertices A, B and C respectively. If$ x_a, x_b and x_c $represent the distance of 'P' from sides BC, AC and AB respectively, then$

$\frac{x_{a}}{H_{a}} + \frac{x_{b}}{H_{b}} + \frac{x_{c}}{H_{c}} is always equal to$

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In the adjacent figure 'P' is any interior point of the equilateral triangle ABC of side length 2 units.If xa , xb and xc represent the distance of P from the sides BC, CA and AB respectively, then xa + xb + xc is equal to

The correct option is B √3Let A1, B1, C1 are the foot of altitudes drawn from 'P' to sides BC, CA and AB respectively. We have,

In the adjacent figure 'P' is any interior point of the equilateral triangle ABC of side length 2 units.

If x_{a ,}x_b and x_c represent the distance of P from the sides BC, CA and AB respectively, then x_a + x_b + x_c is equal to

The correct option is B
√3

Let A₁, B₁, C₁ are the foot of altitudes drawn from 'P' to sides BC, CA and AB respectively. We have,