Answer:
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: <em>A = a * (9 + b)</em>, where <em>a</em> is the unknown base and <em>9 + b</em> 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: <em>a * b</em>, where <em>a</em> is the unknown base and <em>b </em>is the unknown height. (Note that we know <em>a</em> is also the base of PXYS because PQRS is a rectangle and XY is parallel to QR; thus XY = QR = <em>a</em>). 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
