Advertisements
Advertisements
प्रश्न
In triangle ABC, ∠B = 90o and D is the mid-point of BC.
Prove that: AC2 = AD2 + 3CD2.
Advertisements
उत्तर
In ΔABC
AB2 + BC2 = AC2
as [BC = 2CD]
AB2 + 4CD2 = AC2 ....(1)
In ΔABD,
AD2 = AB2 + BD2 = AB2 + CD2 ....(2)
Subtracting (1) and (2)
AC2 - AD2 = AB2 + 4CD2 - (AB2 + CD2)
AC2 - AD2 = 3CD2
AC2 = AD2 + 3CD2
Hence proved.
APPEARS IN
संबंधित प्रश्न
PQR is a triangle right angled at P and M is a point on QR such that PM ⊥ QR. Show that PM2 = QM . MR
ABC is an isosceles triangle right angled at C. Prove that AB2 = 2AC2
A ladder 10 m long reaches a window 8 m above the ground. Find the distance of the foot of the ladder from base of the wall.
Prove that, in a right-angled triangle, the square of the hypotenuse is equal to the sum of the square of remaining two sides.
In the given figure, M is the midpoint of QR. ∠PRQ = 90°. Prove that, PQ2 = 4PM2 – 3PR2.
Two poles of heights 6 m and 11 m stand vertically on a plane ground. If the distance between their feet is 12 m;
find the distance between their tips.
AD is drawn perpendicular to base BC of an equilateral triangle ABC. Given BC = 10 cm, find the length of AD, correct to 1 place of decimal.
In triangle ABC, AB = AC = x, BC = 10 cm and the area of the triangle is 60 cm2.
Find x.
The sides of a certain triangle is given below. Find, which of them is right-triangle
6 m, 9 m, and 13 m
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, 6, 7
Find the length of the perpendicular of a triangle whose base is 5cm and the hypotenuse is 13cm. Also, find its area.
Calculate the area of a right-angled triangle whose hypotenuse is 65cm and one side is 16cm.
In a triangle ABC, AC > AB, D is the midpoint BC, and AE ⊥ BC. Prove that: AC2 = AD2 + BC x DE + `(1)/(4)"BC"^2`
AD is perpendicular to the side BC of an equilateral ΔABC. Prove that 4AD2 = 3AB2.
In a triangle ABC right angled at C, P and Q are points of sides CA and CB respectively, which divide these sides the ratio 2 : 1.
Prove that : 9(AQ2 + BP2) = 13AB2
If ΔABC ~ ΔPQR, `("ar" triangle "ABC")/("ar" triangle "PQR") = 9/4` and AB = 18 cm, then the length of PQ is ______.
Foot of a 10 m long ladder leaning against a vertical wall is 6 m away from the base of the wall. Find the height of the point on the wall where the top of the ladder reaches.
The perimeter of the rectangle whose length is 60 cm and a diagonal is 61 cm is ______.
Two rectangles are congruent, if they have same ______ and ______.
