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
A man goes 10 m due east and then 24 m due north. Find the distance from the starting point
Sides of triangles are given below. Determine it is a right triangles? In case of a right triangle, write the length of its hypotenuse. 3 cm, 8 cm, 6 cm
Sides of triangle are given below. Determine it is a right triangle or not? In case of a right triangle, write the length of its hypotenuse. 50 cm, 80 cm, 100 cm
In Figure, ABD is a triangle right angled at A and AC ⊥ BD. Show that AD2 = BD × CD
The perpendicular from A on side BC of a Δ ABC intersects BC at D such that DB = 3CD . Prove that 2AB2 = 2AC2 + BC2.
Which of the following can be the sides of a right triangle?
2 cm, 2 cm, 5 cm
In the case of right-angled triangles, identify the right angles.
Identify, with reason, if the following is a Pythagorean triplet.
(10, 24, 27)
In the figure: ∠PSQ = 90o, PQ = 10 cm, QS = 6 cm and RQ = 9 cm. Calculate the length of PR.
Choose the correct alternative:
In right-angled triangle PQR, if hypotenuse PR = 12 and PQ = 6, then what is the measure of ∠P?
Find the value of (sin2 33 + sin2 57°)
If P and Q are the points on side CA and CB respectively of ΔABC, right angled at C, prove that (AQ2 + BP2 ) = (AB2 + PQ2)
The sides of the triangle are given below. Find out which one is the right-angled triangle?
11, 12, 15
The sides of the triangle are given below. Find out which one is the right-angled triangle?
1.5, 1.6, 1.7
The foot of a ladder is 6m away from a wall and its top reaches a window 8m above the ground. If the ladder is shifted in such a way that its foot is 8m away from the wall to what height does its tip reach?
In a triangle ABC, AC > AB, D is the midpoint BC, and AE ⊥ BC. Prove that: AB2 = AD2 - BC x CE + `(1)/(4)"BC"^2`
Find the unknown side in the following triangles
For going to a city B from city A, there is a route via city C such that AC ⊥ CB, AC = 2x km and CB = 2(x + 7) km. It is proposed to construct a 26 km highway which directly connects the two cities A and B. Find how much distance will be saved in reaching city B from city A after the construction of the highway.
Prove that the area of the semicircle drawn on the hypotenuse of a right angled triangle is equal to the sum of the areas of the semicircles drawn on the other two sides of the triangle.
Two squares having same perimeter are congruent.
Two poles of 10 m and 15 m stand upright on a plane ground. If the distance between the tops is 13 m, find the distance between their feet.
