Question

The diagonals PR and SQ of a rhombus PQRS interest each other at point o. it is given that OP =(4a-5)cm OR=25cm OS=(a+b)cm OQ =12 cm find a and b.

Answer 1

Given in the sum

Diagonals PR and SQ intersect at o

OP=(4a-5)cm

OR=25 cm

OS =(a+b) cm

OQ=12 cm

To find:

a and b

Solution:

Since diagonals of rhombus bisect each other into equal parts

So,

OP=OR

OS=OQ

therefore,

since,

OP = OQ

(4a-5) = 25

4a = 30

a=30/4=7.5

OP=4×7.5-5

OP=25

OS=OQ

(a+b)= 12

7.5+b=12

b=12-7.5 =4.5

We get a=7.5  

             b = 4.5

Answer 2

Given:
PQRS is a rhombus
Diagonals PR and SQ intersect at o
OP=(4a-5)cm
OR=25 cm
OS =(a+b) cm
OQ=12 cm
To find:
a and b
Solution:
since diagonals of rhombus bisect each other into equal parts
so,
OP=OR
OS=OQ
therefore,
since,
OP=OQ
(4a-5)=25
4a=30
a=30/4=7.5
OP=4×7.5-5
OP=25
OS=OQ
(a+b)= 12
7.5+b=12
b=12-7.5
=4.5
so a=7.5 ,b=4.5