Advertisements
Advertisements
Question
In the right-angled ∆PQR, ∠ P = 90°. If l(PQ) = 24 cm and l(PR) = 10 cm, find the length of seg QR.
Advertisements
Solution
In the right-angled triangle PQR, ∠P = 90°. Hence, side QR is the hypotenuse.
According to Pythagoras' theorem,
l(QR)2 = l(PQ)2 + l(PR)2
⇒ l(QR)2 = (24)2 + (10)2
⇒ l(QR)2 = 576 + 100
⇒ l(QR)2 = 676
⇒ l(QR)2 = (26)2
⇒ l(QR) = 26
∴ Length of seg QR = 26 cm.
RELATED QUESTIONS
A man goes 10 m due east and then 24 m due north. Find the distance from the starting point
In Figure, ABD is a triangle right angled at A and AC ⊥ BD. Show that AB2 = BC × BD
In the given figure, AD is a median of a triangle ABC and AM ⊥ BC. Prove that:
`"AC"^2 = "AD"^2 + "BC"."DM" + (("BC")/2)^2`
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, in a right-angled triangle, the square of the hypotenuse is equal to the sum of the square of remaining two sides.
In figure AB = BC and AD is perpendicular to CD.
Prove that: AC2 = 2BC. DC.
∆ABC is right-angled at C. If AC = 5 cm and BC = 12 cm. find the length of AB.
The perpendicular PS on the base QR of a ∆PQR intersects QR at S, such that QS = 3 SR. Prove that 2PQ2 = 2PR2 + QR2
If in a ΔPQR, PR2 = PQ2 + QR2, then the right angle of ∆PQR is at the vertex ________
In a right angled triangle, the hypotenuse is the greatest side
