Question

perimeter of a rhombus is 146 cm and length of one of its diagonal is 48 cm find the length of other diagonal​

Answer 1

Given

• Perimeter Of Rhombus = 146 cm
• Diagonal = 48 cm

To Find

• Length of Other Diagonal

Solution

We Know That

• All Side Are Equal in rhombus .

• $\sf \: Length \: of \: each \: Side \: = \: \dfrac{146}{4} \\ \sf= 36 .5cm$

$\sf \: Hence, \: length \: of \: each \: side \: of \: the \: rhombus \:  =36.5 \:  cm$

In a rhombus, the diagonals bisect each other at 90°.

O is the midpoint of AC and BD.

• But BD = 48 cmOB= OD= 24cm

Now In ∆ AOB We have,

$\sf \angle \: AOB \: = 90^{0}$

By Pythagoras Theorem

$\sf AB²=AO²+OB²$

$\sf 36.5²=AO²+24²$

$\sf 1332.25=AO²+576$

$\sf AO²= 1332.25-576$

$\sf AO²= 756.25$

$\sf AO= \sqrt{756.25}$

$\sf AO=27.5 cm$

AC= 55 cm

• $\sf Length~ of ~other~ Diagonal ~AC~=~ 55 cm.$

Figure Of Rhombus

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\put(0,0){\line(1,3){1.5}}\put(0,0){\line(1,0){5}}\put(5,0){\line(1,3){1.5}}\put(1.5,4.5){\line(1,0){5}}\qbezier(1.56,4.5)(1.56,4.5)(5,0)\qbezier(6.45,4.5)(6.45,4.5)(0,0)\put(-0.5,-0.5){\sf B}\put(1,4.8){\sf A}\put(5.2,-0.5){\sf C}\put(6.7,4.75){\sf D}\put(3,1.6){\sf O}\end{picture}$

Answer 2

Let PQRS be the rhombus as sh.own in the fi.gure.

gure. Since the length of all sides of a rhombus are equal, Perimeter =4× length of one side ⇒4×PQ=146 cm⇒PQ=36.5 cm

gure. Since the length of all sides of a rhombus are equal, Perimeter =4× length of one side ⇒4×PQ=146 cm⇒PQ=36.5 cmHence, length of each side of the rhombus =36.5 cm

gure. Since the length of all sides of a rhombus are equal, Perimeter =4× length of one side ⇒4×PQ=146 cm⇒PQ=36.5 cmHence, length of each side of the rhombus =36.5 cmIn a rhombus, the diagonals bisect each other at 90

gure. Since the length of all sides of a rhombus are equal, Perimeter =4× length of one side ⇒4×PQ=146 cm⇒PQ=36.5 cmHence, length of each side of the rhombus =36.5 cmIn a rhombus, the diagonals bisect each other at 90 0

gure. Since the length of all sides of a rhombus are equal, Perimeter =4× length of one side ⇒4×PQ=146 cm⇒PQ=36.5 cmHence, length of each side of the rhombus =36.5 cmIn a rhombus, the diagonals bisect each other at 90 0

gure. Since the length of all sides of a rhombus are equal, Perimeter =4× length of one side ⇒4×PQ=146 cm⇒PQ=36.5 cmHence, length of each side of the rhombus =36.5 cmIn a rhombus, the diagonals bisect each other at 90 0 Referring the diagram, if PR=55 cm, then OP=27.5 cm, OQ=

gure. Since the length of all sides of a rhombus are equal, Perimeter =4× length of one side ⇒4×PQ=146 cm⇒PQ=36.5 cmHence, length of each side of the rhombus =36.5 cmIn a rhombus, the diagonals bisect each other at 90 0 Referring the diagram, if PR=55 cm, then OP=27.5 cm, OQ= 2

gure. Since the length of all sides of a rhombus are equal, Perimeter =4× length of one side ⇒4×PQ=146 cm⇒PQ=36.5 cmHence, length of each side of the rhombus =36.5 cmIn a rhombus, the diagonals bisect each other at 90 0 Referring the diagram, if PR=55 cm, then OP=27.5 cm, OQ= 2SQ

gure. Since the length of all sides of a rhombus are equal, Perimeter =4× length of one side ⇒4×PQ=146 cm⇒PQ=36.5 cmHence, length of each side of the rhombus =36.5 cmIn a rhombus, the diagonals bisect each other at 90 0 Referring the diagram, if PR=55 cm, then OP=27.5 cm, OQ= 2SQ

gure. Since the length of all sides of a rhombus are equal, Perimeter =4× length of one side ⇒4×PQ=146 cm⇒PQ=36.5 cmHence, length of each side of the rhombus =36.5 cmIn a rhombus, the diagonals bisect each other at 90 0 Referring the diagram, if PR=55 cm, then OP=27.5 cm, OQ= 2SQ

gure. Since the length of all sides of a rhombus are equal, Perimeter =4× length of one side ⇒4×PQ=146 cm⇒PQ=36.5 cmHence, length of each side of the rhombus =36.5 cmIn a rhombus, the diagonals bisect each other at 90 0 Referring the diagram, if PR=55 cm, then OP=27.5 cm, OQ= 2SQ Since, triangle

gure. Since the length of all sides of a rhombus are equal, Perimeter =4× length of one side ⇒4×PQ=146 cm⇒PQ=36.5 cmHence, length of each side of the rhombus =36.5 cmIn a rhombus, the diagonals bisect each other at 90 0 Referring the diagram, if PR=55 cm, then OP=27.5 cm, OQ= 2SQ Since, triangle =24cm

gure. Since the length of all sides of a rhombus are equal, Perimeter =4× length of one side ⇒4×PQ=146 cm⇒PQ=36.5 cmHence, length of each side of the rhombus =36.5 cmIn a rhombus, the diagonals bisect each other at 90 0 Referring the diagram, if PR=55 cm, then OP=27.5 cm, OQ= 2SQ Since, triangle =24cmSQ=48 cm

gure. Since the length of all sides of a rhombus are equal, Perimeter =4× length of one side ⇒4×PQ=146 cm⇒PQ=36.5 cmHence, length of each side of the rhombus =36.5 cmIn a rhombus, the diagonals bisect each other at 90 0 Referring the diagram, if PR=55 cm, then OP=27.5 cm, OQ= 2SQ Since, triangle =24cmSQ=48 cm Hence, length of the other diagonal =48 cm