In equilateral triangle ABC with interior point D, if the perpendicular distances from D to the sides of 4,5, and 6, respectively, are given, then fin

Monjur Alahi

In equilateral triangle ABC with interior point D, if the perpendicular distances from D to the sides of 4,5, and 6, respectively, are given, then find the area of ` A B Cdot`


0 like 0 dislike
1 views
Share with your friends

1 Answers

Salim Ahmed Kawsar

Call

Let the side equilateral triangleABC be a
Area of triangle, `Delta = (a xx 4 + a xx 5 + a xx 6)/(2)`
or `(a (4 + 5 + 6))/(2) = (sqrt3)/(4) a^(2)`
or `(15)/(2) = (sqrt3a)/(4)`
or `a = (30)/(sqrt3) = 10 sqrt3`
or `Delta = (sqrt3)/(4) xx 100 xx 3`
`= 75 sqrt3`

0 like 0 dislike
1 views
Talk Doctor Online in Bissoy App
The distance between the two lines represented by the sides of an equilateral triangle a right-angled triangle an isosceles triangle none of these

Correct Answer - 1 `9x^(2)-24xy+16y^(2)-12x+16y-12=0` or `(3x-4y+2)(3x-4y-6)=0` Hence , the distance between the lines is `(|6-(-2)|)/(5)=(8)/(5)`.

2 Answers 1 views
`A (veca), B (vecb) and C (vecc)` are the vertices of triangle ABC and `R(vecr)` is any point in the plane of triangle ABC, then `vecr, (veca xx vecb

Correct Answer - b A vector perpendicular to the plane of ` A(veca) , B(vecb) and C(vecc)` is `(vecb -veca) xx (vecc-veca) = vecaxxvecb +vecb xx vecc +vecc xx veca` Now...

2 Answers 1 views
If the distances of the vertices of a triangle =ABC from the points of contacts of the incercle with sides are `alpha,betaa n dgamma` then prove that

We know that distances of the vertices of a triangle from the points of contract to the incircle are `s - a, s- b, s- c`. Thus, `alpha = s...

2 Answers 1 views
The sides of a triangle are in A.P. and its area is `(3)/(5)` th of an equilateral triangle of the same perimeter. Find the greatest angle of the tria

Correct Answer - `120^(@)` Let the sides be `x - d, x, x + d`. Then `s = (3x)/(2), (s -a) = (x)/(2) + d`, `(s-b) = (x)/(2), (s-c) = (x)/(2)...

2 Answers 1 views
In triangle ABC, `R (b + c) = a sqrt(bc)`, where R is the circumradius of the triangle. Then the triangle is

Correct Answer - C `R(b +c) = a sqrt(bc) = 2R sin A sqrt(bc)` `:. sin A = (b +c)/(2sqrt(bc))` Now `sin A le 1` `rArr (b + c)/(2sqrt(bc)) le 1`...

2 Answers 1 views
If `R_(1)` is the circumradius of the pedal triangle of a given triangle ABC, and `R_(2)` is the circumradius of the pedal triangle of the pedal trian

Correct Answer - B Circumradius of triangle ABC, R = 5 `:.` Circumradius of pedal triangle, `R_(1) = 5//2` and so on. Now, `underset(i=1)overset(oo)sum R_(i) + R_(1) + R_(2) + R_(3)...

2 Answers 1 views
ABC is an equilateral triangle of side 10 m and D is the midpoint of BC. Charges of `+100 C, -100 C " and +75 C` are placed at B, C and D respectively

Correct Answer - `1.27 xx 10^(10)N,`" at a angle of" `45^(@)`" with the horiontal"

2 Answers 1 views
Each side of an equilateral triand 12 is \( 24 cm \) the mid - point of its sides are joined to form another tranpla this brress is doins centinuously infinite 46. The perimeter of 7 th triangle is \( ( \) in \( cm ) \) a) \( \frac{3}{4} \) b) \( \frac{5}{8} \) c) \( \frac{9}{8} \) d) \( \frac{7}{8} \) 47. The sum of perimeter of all triangle is (in \( cm \) ) a) 144 b) 625 c) 400 d) 169 48. The area of all the triangle is (in sq cm) a) 576 b) \( 144 \sqrt{3} \) c) \( 169 \sqrt{3} \) d) \( 192 \sqrt{3} \) 49. The sum of perimeter of first 6 triangle is (in \( cm \) ) a) 120 b) \( \frac{567}{4} \) c) \( \frac{569}{4} \) d) 144 50. The side of the 5th triangle is (in \( cm \) ) a) 6 b) \( 1.5 \) c) \( 0.75 \) d) 3

post the question correctly

2 Answers 1 views
One side of an equilateral triangle is 36 cm. The mid-points of its sides are joined to form another triangle. Again another triangle is formed by joi

Correct Answer - `432sqrt3 cm^(2)`

2 Answers 2 views
The midpoints of the sides BC, CA and AB of a `triangle ABC` are D(2,1), E(-5,7)and F-5, -5) respectively. Find the equations of the sides of `triangl

Correct Answer - x-2=0, 6x-7y+79=0, 6x+7y+65=0

2 Answers 1 views
X