Some Question and Their Alternative Answer Are Given. Altitude on the Hypotenuse of a Right Angled Triangle Divides It in Two Parts of Lengths 4 Cm and 9 Cm. Find the Length of the Altitude. - Geometry Mathematics 2

Advertisements
Advertisements
MCQ

Some question and their alternative answer are given. Select the correct alternative.

Altitude on the hypotenuse of a right angled triangle divides it in two parts of lengths 4 cm and 9 cm. Find the length of the altitude.

Options

  • 9 cm 

  • 4 cm

  • 6 cm  

  • \[2\sqrt{6}\] cm

Advertisements

Solution

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.

\[\therefore {AD}^2 = CD \times DB\]
\[ = 4 \times 9\]
\[ = 36\]
\[ \Rightarrow AD = 6 cm\]

Hence, the  correct option is 6 cm.

  Is there an error in this question or solution?
Chapter 2: Pythagoras Theorem - Problem Set 2 [Page 43]

RELATED QUESTIONS

Adjacent sides of a parallelogram are 11 cm and 17 cm. If the length of one of its diagonal is 26 cm, find the length of the other.


In ∆ABC, point M is the midpoint of side BC. If, AB+ AC= 290 cm2, AM = 8 cm, find BC.


Some question and their alternative answer are given. Select the correct alternative.

Out of the following which is the Pythagorean triplet?


Some question and their alternative answer are given.

In a right-angled triangle, if sum of the squares of the sides making right angle is 169 then what is the length of the hypotenuse?


Some question and their alternative answer are given. Select the correct alternative.

Height and base of a right angled triangle are 24 cm and 18 cm find the length of its hypotenuse


Do sides 7 cm, 24 cm, 25 cm form a right angled triangle ? Give reason


Find the length a diagonal of a rectangle having sides 11 cm and 60 cm.


A side of an isosceles right angled triangle is x. Find its hypotenuse. 


Prove that the sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares of its sides.


Sum of the squares of adjacent sides of a parallelogram is 130 sq.cm and length of one of its diagonals is 14 cm. Find the length of the other diagonal.


Seg PM is a median of ∆PQR. If PQ = 40, PR = 42 and PM = 29, find QR.


Seg AM is a median of ∆ABC. If AB = 22, AC = 34, BC = 24, find AM


If hypotenuse of a right angled triangle is 5 cm, find the radius of
the circle passing through all vertices of the triangle.


In ΔPQR, seg PM is the median. If PM = 9, PQ2 + PR2 = 290, Find QR. 


In ΔABC, seg AP is a median. If BC = 18, AB2 + AC2 = 260, then find the length of AP. 


Choose the correct alternative:

Out of given triplets, which is not a Pythagoras triplet?


"The diagonals bisect each other at right angles." In which of the following quadrilaterals is the given property observed?


Which of the following figure is formed by joining the mid-points of the adjacent sides of a square?


Share
Notifications



      Forgot password?
Use app×