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a cm
R
Dia
dra
In the diagram shown,
PQRS is a rectangle,
XY is parallel to PS,
RY = 9 cm,
Area of PQRS = 84 cm,
Area of PXYS = 21 cm.
Work out the values of a and b.
You must show all your working.
9 cm
ү
bcm
P
S

The answer is below

Step-by-step explanation:

PQRS is a rectangle. The length of rectangle PQRS = 9 cm + b cm = (9 + b)cm

The breadth of PQRS = a. Hence:

Area of PQRS = length * breadth = (9 + b)(a) = 9a + ab

but Area of PQRS = 84 cm²

9a + ab = 84          (1)

In rectangle PXYS, length = QR = a cm, breadth = YS = b cm

Hence area of PXYS = length * breadth = (a)(b) = ab

But Area of PXYS = 21 cm²

ab = 21         (2)

substitute ab = 21 in equation 1:

9a + 21 = 84

9a = 84 - 21

9a = 63

a = 7 cm

ab = 21

7b = 21

b = 3 cm

Therefore a = 7cm, b = 3 cm

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