Advertisements
Advertisements
प्रश्न
In ΔMNP, ∠MNP = 90˚, seg NQ ⊥ seg MP, MQ = 9, QP = 4, find NQ.
Advertisements
उत्तर
NQ2 = `sqrt(MQ xx QP)` ......(Theorem of Geometric mean)
= `sqrt(9 xx 4)`
= 36
∴ NQ = `sqrt(36)`
= 6 unit
संबंधित प्रश्न
Side of a triangle is given, determine it is a right triangle.
`(2a – 1) cm, 2\sqrt { 2a } cm, and (2a + 1) cm`
In a right triangle ABC right-angled at C, P and Q are the points on the sides CA and CB respectively, which divide these sides in the ratio 2 : 1. Prove that
`(i) 9 AQ^2 = 9 AC^2 + 4 BC^2`
`(ii) 9 BP^2 = 9 BC^2 + 4 AC^2`
`(iii) 9 (AQ^2 + BP^2 ) = 13 AB^2`
PQR is a triangle right angled at P and M is a point on QR such that PM ⊥ QR. Show that PM2 = QM . MR
In Figure, ABD is a triangle right angled at A and AC ⊥ BD. Show that AB2 = BC × BD
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.
A tree is broken at a height of 5 m from the ground and its top touches the ground at a distance of 12 m from the base of the tree. Find the original height of the tree.
Which of the following can be the sides of a right triangle?
2 cm, 2 cm, 5 cm
In the case of right-angled triangles, identify the right angles.
Find the length diagonal of a rectangle whose length is 35 cm and breadth is 12 cm.
In a rectangle ABCD,
prove that: AC2 + BD2 = AB2 + BC2 + CD2 + DA2.
In triangle ABC, ∠B = 90o and D is the mid-point of BC.
Prove that: AC2 = AD2 + 3CD2.
M andN are the mid-points of the sides QR and PQ respectively of a PQR, right-angled at Q.
Prove that:
(i) PM2 + RN2 = 5 MN2
(ii) 4 PM2 = 4 PQ2 + QR2
(iii) 4 RN2 = PQ2 + 4 QR2(iv) 4 (PM2 + RN2) = 5 PR2
Show that the triangle ABC is a right-angled triangle; if: AB = 9 cm, BC = 40 cm and AC = 41 cm
The sides of the triangle are given below. Find out which one is the right-angled triangle?
1.5, 1.6, 1.7
A right triangle has hypotenuse p cm and one side q cm. If p - q = 1, find the length of third side of the triangle.
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`
If in a ΔPQR, PR2 = PQ2 + QR2, then the right angle of ∆PQR is at the vertex ________
If ‘l‘ and ‘m’ are the legs and ‘n’ is the hypotenuse of a right angled triangle then, l2 = ________
If length of sides of a triangle are a, b, c and a2 + b2 = c2, then which type of triangle it is?
Two squares having same perimeter are congruent.
Height of a pole is 8 m. Find the length of rope tied with its top from a point on the ground at a distance of 6 m from its bottom.
