English

The Length of the Diagonals of Rhombus Are 24cm and 10cm. Find Each Side of the Rhombus. - Mathematics

Advertisements
Advertisements

Question

The length of the diagonals of rhombus are 24cm and 10cm. Find each side of the rhombus.

Sum

Solution

It is given that the diagonals of a rhombus are of length 14cm and 10cm respectively
∴ d1 = 24cm, d2 = 10cm
The diagonals of a rhombus bisect each other

∴ `("d"_1/2)^2 + ("d"_2/2)^2` = side2

⇒ side2
= 122 + 52
= 144 + 25
= 132
⇒ Side = 13
Thus, each side of the rhombus is of length 13cm.

shaalaa.com
  Is there an error in this question or solution?
Chapter 17: Pythagoras Theorem - Exercise 17.1

APPEARS IN

Frank Mathematics [English] Class 9 ICSE
Chapter 17 Pythagoras Theorem
Exercise 17.1 | Q 10

RELATED QUESTIONS

PQR is a triangle right angled at P and M is a point on QR such that PM ⊥ QR. Show that PM2 = QM . MR


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.


Prove that the points A(0, −1), B(−2, 3), C(6, 7) and D(8, 3) are the vertices of a rectangle ABCD?


Identify, with reason, if the following is a Pythagorean triplet.
(3, 5, 4)


In the given figure, M is the midpoint of QR. ∠PRQ = 90°. Prove that, PQ= 4PM– 3PR2.


In an isosceles triangle ABC; AB = AC and D is the point on BC produced.
Prove that: AD2 = AC2 + BD.CD.


Diagonals of rhombus ABCD intersect each other at point O.

Prove that: OA2 + OC2 = 2AD2 - `"BD"^2/2`


Triangle ABC is right-angled at vertex A. Calculate the length of BC, if AB = 18 cm and AC = 24 cm.


A boy first goes 5 m due north and then 12 m due east. Find the distance between the initial and the final position of the boy.


In the right-angled ∆LMN, ∠M = 90°. If l(LM) = 12 cm and l(LN) = 20 cm, find the length of seg MN.


In ΔABC, AD is perpendicular to BC. Prove that: AB2 + CD2 = AC2 + BD2


In a triangle ABC, AC > AB, D is the midpoint BC, and AE ⊥ BC. Prove that: AB2 + AC2 = 2AD2 + `(1)/(2)"BC"^2`


In the given figure, PQ = `"RS"/(3)` = 8cm, 3ST = 4QT = 48cm.
SHow that ∠RTP = 90°.


Choose the correct alternative:

If length of sides of a triangle are a, b, c and a2 + b2 = c2, then which type of triangle it is?


From the given figure, in ∆ABQ, if AQ = 8 cm, then AB =?


From given figure, In ∆ABC, If AC = 12 cm. then AB =?


Activity: From given figure, In ∆ABC, ∠ABC = 90°, ∠ACB = 30°

∴ ∠BAC = `square`

∴ ∆ABC is 30° – 60° – 90° triangle

∴ In ∆ABC by property of 30° – 60° – 90° triangle.

∴ AB = `1/2` AC and `square` = `sqrt(3)/2` AC

∴ `square` = `1/2 xx 12` and BC = `sqrt(3)/2 xx 12`

∴ `square` = 6 and BC = `6sqrt(3)`


Lengths of sides of a triangle are 3 cm, 4 cm and 5 cm. The triangle is ______.


The perimeter of the rectangle whose length is 60 cm and a diagonal is 61 cm is ______.


Two poles of 10 m and 15 m stand upright on a plane ground. If the distance between the tops is 13 m, find the distance between their feet.


The foot of a ladder is 6 m away from its wall and its top reaches a window 8 m above the ground. If the ladder is shifted in such a way that its foot is 8 m away from the wall, to what height does its top reach?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×