Question

In figure 2.17, Z MNP = 90
seg NQ Lseg MP, MQ = 9,
QP = 4, find NQ.व्हाट इज द मेट्रिक मींस फार्मूला ​

Answer 1

Correct Question:

In figure, ∠ MNP = 90°, seg NQ ⊥ seg MP,

MQ = 9,

QP = 4, find NQ.

What is the geometric mean formula?

Answer:

The length of the segment NQ is 6 units.

Step-by-step-explanation:

NOTE: Refer to the attachment for the diagram.

In Δ MNP,

∠ MNP = 90° - - - [ Given ]

Seg NQ ⊥ seg MP - - - [ Given ]

Now, by geometric mean property,

NQ² = MQ × PQ

➞ NQ² = 9 × 4

➞ NQ² = 36

➞ NQ = $\pm$ 6

- - - [ Taking square roots of both sides ]

But, length can't be negative.

∴ NQ = 6 units

Additional Information:

1. Geometric mean theorem:

1. The perpendicular segment from the vertex opposite to hypotenuse in a right angled triangle is called the geometric mean of the triangle.

2. It divides the hypotenuse in two parts.

3. The square of the segment is equal to the product of the two parts in which the hypotenuse is divided.

Answer 2

Answer:

We know that,

In a right angled triangle, the perpendicular segment to the hypotenuse from the opposite vertex, is the geometric mean of the segments into which the hypotenuse is divided.

∴ QN²=MQ×QP

=9×4

QN=√ 36

=√ 36

=6

Hence, NQ = 6.