Advertisements
Advertisements
प्रश्न
In equilateral Δ ABC, AD ⊥ BC and BC = x cm. Find, in terms of x, the length of AD.
Advertisements
उत्तर १
In equilateral Δ ABC, AD ⊥ BC.
Therefore, BC = x cm.
Area of equilateral ΔABC = `sqrt3/4 xx "side"^2 = 1/2 xx "base" xx "height"`
= `sqrt3/4 xx x^2 = 1/2 xx x xx "AD"`
AD = `sqrt3/2 x`
उत्तर २
In △ADC and △ADB,
AD = AD ...(Common)
∠ADB = ∠ADC ...(Each 90°)
AB = AC ....(Given, ABC is an equilateral triangle)
Thus, △ADC ≅ △ADB
BD = DC = `1/2`BC ...(By cpct)
Hence, BD = `1/2`x
In △ADB,
∠D = 90°
△ADB is right angle triangle,
by Pythagoras theorem,
AB2 = BD2 + AD2
`x^2 = (1/2x)^2 + "AD"^2`
`"AD"^2 = x^2 − (x^2)/4`
`"AD"^2 = 3/4x^2`
`"AD" = (sqrt(3))/2x`
APPEARS IN
संबंधित प्रश्न
ABCD is a rhombus. Prove that AB2 + BC2 + CD2 + DA2= AC2 + BD2
In the given figure, ABC is a triangle in which ∠ABC < 90° and AD ⊥ BC. Prove that AC2 = AB2 + BC2 − 2BC.BD.
In the given figure, AD is a median of a triangle ABC and AM ⊥ BC. Prove that:
`"AC"^2 = "AD"^2 + "BC"."DM" + (("BC")/2)^2`
In the given figure, ∠DFE = 90°, FG ⊥ ED, If GD = 8, FG = 12, find (1) EG (2) FD and (3) EF
O is any point inside a rectangle ABCD.
Prove that: OB2 + OD2 = OC2 + OA2.
In a rectangle ABCD,
prove that: AC2 + BD2 = AB2 + BC2 + CD2 + DA2.
In the following Figure ∠ACB= 90° and CD ⊥ AB, prove that CD2 = BD × AD
Triangle PQR is right-angled at vertex R. Calculate the length of PR, if: PQ = 34 cm and QR = 33.6 cm.
A boy first goes 5 m due north and then 12 m due east. Find the distance between the initial and the final position of the boy.
In the figure below, find the value of 'x'.
Find the Pythagorean triplet from among the following set of numbers.
3, 4, 5
Find the Pythagorean triplet from among the following set of numbers.
2, 4, 5
Find the Pythagorean triplet from among the following set of numbers.
4, 5, 6
Find the length of the perpendicular of a triangle whose base is 5cm and the hypotenuse is 13cm. Also, find its area.
Each side of rhombus is 10cm. If one of its diagonals is 16cm, find the length of the other diagonals.
In the given figure, PQ = `"RS"/(3)` = 8cm, 3ST = 4QT = 48cm.
SHow that ∠RTP = 90°.
An isosceles triangle has equal sides each 13 cm and a base 24 cm in length. Find its height
From the given figure, in ∆ABQ, if AQ = 8 cm, then AB = ?
Two squares having same perimeter are congruent.
Points A and B are on the opposite edges of a pond as shown in the following figure. To find the distance between the two points, the surveyor makes a right-angled triangle as shown. Find the distance AB.
