Advertisements
Advertisements
Question

In ΔMNP, ∠MNP = 90˚, seg NQ ⊥ seg MP, MQ = 9, QP = 4, find NQ.
Advertisements
Solution
NQ2 = `sqrt(MQ xx QP)` ......(Theorem of Geometric mean)
= `sqrt(9 xx 4)`
= 36
∴ NQ = `sqrt(36)`
= 6 unit
RELATED QUESTIONS
The points A(4, 7), B(p, 3) and C(7, 3) are the vertices of a right traingle ,right-angled at B. Find the values of p.
Sides of triangle are given below. Determine it is a right triangle or not? In case of a right triangle, write the length of its hypotenuse. 13 cm, 12 cm, 5 cm
In Figure, ABD is a triangle right angled at A and AC ⊥ BD. Show that AB2 = BC × BD

In Figure, ABD is a triangle right angled at A and AC ⊥ BD. Show that AD2 = BD × CD

Two poles of heights 6 m and 11 m stand on a plane ground. If the distance between the feet of the poles is 12 m, find the distance between their tops.
In the given figure, M is the midpoint of QR. ∠PRQ = 90°. Prove that, PQ2 = 4PM2 – 3PR2.

In the following figure, OP, OQ, and OR are drawn perpendiculars to the sides BC, CA and AB respectively of triangle ABC.
Prove that: AR2 + BP2 + CQ2 = AQ2 + CP2 + BR2

Find the value of (sin2 33 + sin2 57°)
Find the Pythagorean triplet from among the following set of numbers.
4, 7, 8
The sides of the triangle are given below. Find out which one is the right-angled triangle?
11, 60, 61
The foot of a ladder is 6m away from a wall and its top reaches a window 8m above the ground. If the ladder is shifted in such a way that its foot is 8m away from the wall to what height does its tip reach?
From a point O in the interior of aΔABC, perpendicular OD, OE and OF are drawn to the sides BC, CA and AB respectively. Prove that: AF2 + BD2 + CE2 = OA2 + OB2 + OC2 - OD2 - OE2 - OF2
If in a ΔPQR, PR2 = PQ2 + QR2, then the right angle of ∆PQR is at the vertex ________
Find the unknown side in the following triangles
In the given figure, ∠T and ∠B are right angles. If the length of AT, BC and AS (in centimeters) are 15, 16, and 17 respectively, then the length of TC (in centimeters) is ______.

A 5 m long ladder is placed leaning towards a vertical wall such that it reaches the wall at a point 4 m high. If the foot of the ladder is moved 1.6 m towards the wall, then find the distance by which the top of the ladder would slide upwards on the wall.
Lengths of sides of a triangle are 3 cm, 4 cm and 5 cm. The triangle is ______.
Two angles are said to be ______, if they have equal measures.
Jiya walks 6 km due east and then 8 km due north. How far is she from her starting place?
The foot of a ladder is 6 m away from its wall and its top reaches a window 8 m above the ground. Find the length of the ladder.
