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a = 7, b = 3

Step-by-step explanation:

The area of a rectangle is base * height. Here, the area of PQRS can be written as: A = a * (9 + b), where a is the unknown base and 9 + b is the unknown height. We set this equal to 84 because that's what's given:

a(9 + b) = 84 = 9a + ab (I just distributed)

Now, we can write the area of PXYS as: a * b, where a is the unknown base and b is the unknown height. (Note that we know a is also the base of PXYS because PQRS is a rectangle and XY is parallel to QR; thus XY = QR = a). We set this equal to 21 because that's the area given:

ab = 21

Now, we can just plug in this value to our first equation:

9a + ab = 9a + 21 = 84

Solving for a, we get a = 7. We plug this back into ab = 21 and find that b = 3.

Thus, our answer is: a = 7, b = 3

a = 7 cm , b = 3 cm

Step-by-step explanation:

PXYS: a × b = 21

ab = 21

PQRS: a × (b + 9) = 84

ab + 9a = 84

21 + 9a = 84

9a = 63

a = 7

7b = 21

b = 3

-2

7 - 9 = -2

reversed:

-2 + 9 = 7