4p² + 5q²-6r² +9 from 3p²- 8q² + 4r² - 2 what will we the solution...
Answers
Step-by-step explanation:
The given points are P(2,-1), Q(3,4), R(-2,3) and S(-3,-2).We have
PQ=
(3−2)
2
+(4+1)
2
=
1
2
+5
2
=
26
units
QR=
(−2−3)
2
+(3−4)
2
=
25+1
=
26
units
RS=
(−3+2)
2
+(−2−3)
2
=
1+25
=
26
units
SP=
(−3−2)
2
+(−2−3)
2
=
26
units
PR=
(−2−2)
2
+(3+1)
2
=
16+16
=4
2
units
and, QS=
(−3−3)
2
+(−2−4)
2
=
36+36
=6
2
units
∴PQ=QR=RS=SP=
26
units
and, PR
=QS
This means that PQRS is quadrilateral whose sides are equal but diagonals are not equal.
Thus, PQRS is a rhombus but not a square.
.Now, Area of rhombus PQRS=
2
1
×(Productoflengthsofdiagonals)
⇒AreaofrhombusPQRS=
2
1
×(PR×QS)
⇒AreaofrhombusPQRS=(
2
1
×4
2
×6
2
The given points are P(2,-1), Q(3,4), R(-2,3) and S(-3,-2).We have
PQ=
(3−2)
2
+(4+1)
2
=
1
2
+5
2
=
26
units
QR=
(−2−3)
2
+(3−4)
2
=
25+1
=
26
units
RS=
(−3+2)
2
+(−2−3)
2
=
1+25
=
26
units
SP=
(−3−2)
2
+(−2−3)
2
=
26
units
PR=
(−2−2)
2
+(3+1)
2
=
16+16
=4
2
units
and, QS=
(−3−3)
2
+(−2−4)
2
=
36+36
=6
2
units
∴PQ=QR=RS=SP=
26
units
and, PR
=QS
This means that PQRS is quadrilateral whose sides are equal but diagonals are not equal.
Thus, PQRS is a rhombus but not a square.
.Now, Area of rhombus PQRS=
2
1
×(Productoflengthsofdiagonals)
⇒AreaofrhombusPQRS=
2
1
×(PR×QS)
⇒AreaofrhombusPQRS=(
2
1
×4
2
×6
2
)sq.units=24sq.units
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the weight in gram of 35 mango