Advertisements
Advertisements
प्रश्न
In the following figure, AD is perpendicular to BC and D divides BC in the ratio 1: 3.
Prove that : 2AC2 = 2AB2 + BC2
Advertisements
उत्तर
Here,
BD : DC = 1 : 3.
⇒ BD = `1/4"BC" and CD = 3/4`BC
AC2 = AD2 + CD2 and AB2 = AD2 + BD2
Therefore,
AC2 - AB2 = CD2 - BD2
= `( 3/4"BC" )^2 - ( 1/4 "BC" )^2 `
= `9/16 "BC"^2 - 1/16 "BC"^2`
= `1/2"BC"^2`
∴ 2AC2 - 2AB2 = BC2
2AC2 = 2AB2 + BC2
Hence proved.
APPEARS IN
संबंधित प्रश्न
ABCD is a rhombus. Prove that AB2 + BC2 + CD2 + DA2= AC2 + BD2
In Figure ABD is a triangle right angled at A and AC ⊥ BD. Show that AC2 = BC × DC
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.
In the given figure, ABC is a triangle in which ∠ABC> 90° and AD ⊥ CB produced. Prove that AC2 = AB2 + BC2 + 2BC.BD.
Prove that the sum of the squares of the diagonals of parallelogram is equal to the sum of the squares of its sides.
PQR is a triangle right angled at P. If PQ = 10 cm and PR = 24 cm, find QR.
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`
=
The sides of a certain triangle is given below. Find, which of them is right-triangle
6 m, 9 m, and 13 m
In the given figure, angle BAC = 90°, AC = 400 m, and AB = 300 m. Find the length of BC.
In the given figure, AD = 13 cm, BC = 12 cm, AB = 3 cm and angle ACD = angle ABC = 90°. Find the length of DC.
Find the Pythagorean triplet from among the following set of numbers.
4, 7, 8
From the given figure, find the length of hypotenuse AC and the perimeter of ∆ABC.
Two poles of height 9m and 14m stand on a plane ground. If the distance between their 12m, find the distance between their tops.
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`
PQR is an isosceles triangle with PQ = PR = 10 cm and QR = 12 cm. Find the length of the perpendicular from P to QR.
Find the unknown side in the following triangles
The hypotenuse of a right angled triangle of sides 12 cm and 16 cm is __________
If length of sides of a triangle are a, b, c and a2 + b2 = c2, then which type of triangle it is?
Jayanti takes shortest route to her home by walking diagonally across a rectangular park. The park measures 60 metres × 80 metres. How much shorter is the route across the park than the route around its edges?
