Advertisements
Advertisements
प्रश्न
ABC is an equilateral triangle of side 2a. Find each of its altitudes.
उत्तर
Let AD be the altitude in the given equilateral triangle, ΔABC.
We know that altitude bisects the opposite side.
∴ BD = DC = a
In ΔADB
∠ADB = 90º
Applying pythagoras theorem we obtain
AD2 + DB2 = AD2
⇒ AD2 + a2 = (2a)2
⇒ AD2 + a2 = 4a2
⇒ AD2 = 3a2
⇒ AD =`asqrt3`
In an equilateral triangle, all the altitudes are equal in length. Therefore, the length of each altitude will be `sqrt3a`
APPEARS IN
संबंधित प्रश्न
In figure, ∠B of ∆ABC is an acute angle and AD ⊥ BC, prove that AC2 = AB2 + BC2 – 2BC × BD
PQR is a triangle right angled at P and M is a point on QR such that PM ⊥ QR. Show that PM2 = QM . MR
A guy wire attached to a vertical pole of height 18 m is 24 m long and has a stake attached to the other end. How far from the base of the pole should the stake be driven so that the wire will be taut?
Which of the following can be the sides of a right triangle?
2.5 cm, 6.5 cm, 6 cm
In the case of right-angled triangles, identify the right angles.
For finding AB and BC with the help of information given in the figure, complete following activity.
AB = BC .......... 
∴ ∠BAC =
∴ AB = BC = × AC
= × `sqrt8`
= × `2sqrt2`
=
In ∆ABC, seg AD ⊥ seg BC, DB = 3CD.
Prove that: 2AB2 = 2AC2 + BC2
In an isosceles triangle, length of the congruent sides is 13 cm and its base is 10 cm. Find the distance between the vertex opposite the base and the centroid.
The sides of the triangle are given below. Find out which one is the right-angled triangle?
1.5, 1.6, 1.7
From the given figure, find the length of hypotenuse AC and the perimeter of ∆ABC.
Rithika buys an LED TV which has a 25 inches screen. If its height is 7 inches, how wide is the screen? Her TV cabinet is 20 inches wide. Will the TV fit into the cabinet? Give reason
