Given:
PQRS is a rectangle and XY is parallel to PS.
RY = 9 cm, QR = a cm and YS = b cm
Area of PQRS = 84 cm²
Area of PXYS = 21 cm²
To find:
The value of a and b.
Solution:
RS = 9 + b
Area of rectangle = length × width
Area of PQRS = QR × RY
QR × RS = 84
[tex]a \times (9 + b) = 84[/tex]
[tex]9a+ab=84[/tex] ----------- (1)
Area of PXYS = XY × PS
XY × PS = 21
[tex]a\times b=21[/tex] (since QR = XY)
[tex]ab=21[/tex] ----------- (2)
Substitute (2) in (1).
[tex]9a+21=84[/tex]
Subtract 21 from both sides, we get
[tex]9a = 63[/tex]
Divide by 9 on both sides, we get
a = 7
Substitute a = 7 in (2).
[tex]7 b=21[/tex]
Divide by 7 on both sides, we get
b = 3
The value of a is 7 cm and b is 3 cm.
