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
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
Which of the following can be the sides of a right triangle?
1.5 cm, 2 cm, 2.5 cm
In the case of right-angled triangles, identify the right angles.
Prove that the points A(0, −1), B(−2, 3), C(6, 7) and D(8, 3) are the vertices of a rectangle ABCD?
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`
=
Find the length diagonal of a rectangle whose length is 35 cm and breadth is 12 cm.
In the figure, given below, AD ⊥ BC.
Prove that: c2 = a2 + b2 - 2ax.
In the following Figure ∠ACB= 90° and CD ⊥ AB, prove that CD2 = BD × AD
Choose the correct alternative:
In right-angled triangle PQR, if hypotenuse PR = 12 and PQ = 6, then what is the measure of ∠P?
The sides of a certain triangle is given below. Find, which of them is right-triangle
16 cm, 20 cm, and 12 cm
In the given figure, angle BAC = 90°, AC = 400 m, and AB = 300 m. Find the length of BC.
The sides of the triangle are given below. Find out which one is the right-angled triangle?
11, 12, 15
From the given figure, find the length of hypotenuse AC and the perimeter of ∆ABC.
Find the length of the hypotenuse of a triangle whose other two sides are 24cm and 7cm.
The perpendicular PS on the base QR of a ∆PQR intersects QR at S, such that QS = 3 SR. Prove that 2PQ2 = 2PR2 + QR2
Find the distance between the helicopter and the ship
From given figure, In ∆ABC, If AC = 12 cm. then AB =?
Activity: From given figure, In ∆ABC, ∠ABC = 90°, ∠ACB = 30°
∴ ∠BAC = `square`
∴ ∆ABC is 30° – 60° – 90° triangle
∴ In ∆ABC by property of 30° – 60° – 90° triangle.
∴ AB = `1/2` AC and `square` = `sqrt(3)/2` AC
∴ `square` = `1/2 xx 12` and BC = `sqrt(3)/2 xx 12`
∴ `square` = 6 and BC = `6sqrt(3)`
The top of a broken tree touches the ground at a distance of 12 m from its base. If the tree is broken at a height of 5 m from the ground then the actual height of the tree is ______.
Two squares are congruent, if they have same ______.
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?
The foot of a ladder is 6 m away from its wall and its top reaches a window 8 m above the ground. If the ladder is shifted in such a way that its foot is 8 m away from the wall, to what height does its top reach?
