Advertisements
Advertisements
प्रश्न
In ∆PQR, PQ = √8 , QR = √5 , PR = √3. Is ∆PQR a right-angled triangle? If yes, which angle is of 90°?
Advertisements
उत्तर
In ∆PQR, PQ = √8 , QR = √5 , PR = √3
Longest side of ∆PQR = PQ = √8
∴ PQ2 = (√8)2 = 8
Now, the sum of the squares of the remaining sides is
QR2 + PR2 = (√5)2 + (√3)2 = 5 + 3 = 8
∴ PQ2 = QR2 + PR2
∴ The square of the longest side is equal to the sum of the squares of the remaining two sides.
by Converse of Pythagoras theorem,
∴ ∆PQR is a right-angled triangle.
Now, PQ is the hypotenuse.
∴ ∠PRQ = 90° ...(Angle opposite to hypotenuse)
∴ ∆PQR is a right-angled triangle in which ∠PRQ is 90°.
APPEARS IN
संबंधित प्रश्न
Sides of the triangle are 7 cm, 24 cm, and 25 cm. Determine whether the triangle is a right-angled triangle or not.
In the rectangle WXYZ, XY + YZ = 17 cm, and XZ + YW = 26 cm. Calculate the length and breadth of the rectangle?
8, 15, 17 is a Pythagorean triplet
Check whether given sides are the sides of right-angled triangles, using Pythagoras theorem
8, 15, 17
Check whether given sides are the sides of right-angled triangles, using Pythagoras theorem
9, 40, 41
Check whether given sides are the sides of right-angled triangles, using Pythagoras theorem
24, 45, 51
The area of a rectangle of length 21 cm and diagonal 29 cm is __________
In right angled triangle, if sum of the squares of the sides of right angle is 169, then what is the length of the hypotenuse?
If the length of diagonal of square is `sqrt(2)`, then what is the length of each side?
If length of both diagonals of rhombus are 60 and 80, then what is the length of side?
In ∆ABC, AB = `6sqrt(3)` cm, AC = 12 cm, and BC = 6 cm then m∠A = ?
If a triangle having sides 50 cm, 14 cm and 48 cm, then state whether given triangle is right angled triangle or not.
A rectangle having dimensions 35 m × 12 m, then what is the length of its diagonal?
In ∆LMN, l = 5, m = 13, n = 12 then complete the activity to show that whether the given triangle is right angled triangle or not.
*(l, m, n are opposite sides of ∠L, ∠M, ∠N respectively)
Activity: In ∆LMN, l = 5, m = 13, n = `square`
∴ l2 = `square`, m2 = 169, n2 = 144.
∴ l2 + n2 = 25 + 144 = `square`
∴ `square` + l2 = m2
∴ By Converse of Pythagoras theorem, ∆LMN is right angled triangle.
In ΔABC, AB = 9 cm, BC = 40 cm, AC = 41 cm. State whether ΔABC is a right-angled triangle or not. Write reason.
In the given figure, triangle PQR is right-angled at Q. S is the mid-point of side QR. Prove that QR2 = 4(PS2 – PQ2).
In a right angled triangle, right-angled at B, lengths of sides AB and AC are 5 cm and 13 cm, respectively. What will be the length of side BC?
