Advertisements
Advertisements
प्रश्न
In an equilateral triangle ABC if AD ⊥ BC, then
विकल्प
5AB2 = 4AD2
3AB2 = 4AD2
4AB2 = 3AD2
2AB2 = 3AD2
उत्तर
∆ABC is an equilateral triangle and `AD ⊥ BC`.
In ∆ABD, applying Pythagoras theorem, we get
`AB^2=AD^2+BD^2`
`AB^2=AD^2+(1/2BC)^2(∵BD=1/2BC)`
`AB^2=AD^2+(1/2AB)^2(∵ AB=BC)`
`AB^2=AD^2+1/2AB^2`
`3AB^2=4AD^2`
We got the result as `b`.
APPEARS IN
संबंधित प्रश्न
In the below figure, If AB || CD, find the value of x.
A vertical stick of length 6 m casts a shadow 4 m long on the ground and at the same time a tower casts a shadow 28 m long. Find the height of the tower.
A ladder is placed in such a way that its foot is at a distance of 15m from a wall and its top reaches a window 20m above the ground. Find the length of the ladder.
In each of the figures [(i)-(iv)] given below, a line segment is drawn parallel to one side of the triangle and the lengths of certain line-segment are marked. Find the value of x in each of the following :
In ∆ABC, P and Q are points on sides AB and AC respectively such that PQ || BC. If AP = 4 cm, PB = 6 cm and PQ = 3 cm, determine BC.
In each of the following figures, you find who triangles. Indicate whether the triangles are similar. Give reasons in support of your answer.
State SSS similarity criterion.
State SAS similarity criterion.
In the given figure, PQ || BC and AP : PB = 1 : 2. Find\[\frac{area \left( ∆ APQ \right)}{area \left( ∆ ABC \right)}\]
If ABC is a right triangle right-angled at B and M, N are the mid-points of AB and BC respectively, then 4(AN2 + CM2) =
