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10. The length of a rectangle is 4r2s5t2 units, and the rectangle’s area is 20r5s7t4 square units. What is the width of the rectangle?`

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Nataliya D. | Patient and effective tutor for your most difficult subject.Patient and effective tutor for your mos...
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ax / ay = ax-y

W = (20r5s7t4) / (4r2s5t2) = (20/4) r5-2 s7-5 t4-2 = 5r3s2t2

Stephen H. | Tutor of Math, Physics and Engineering ... available onlineTutor of Math, Physics and Engineering ....
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Since the area of a rectangle is related to it's length times width (A = L*W), then that formula can be rearranged to show that the width is the Area divided by the Length (W=A/L). So:

W = 20r5s7t4/4r2s5t2 (substitute the given expressions for A and L)

W = 20*5*7*4*r*s*t / 4*2*5*2*r*s*t (rearrange to make it easier to see that r, s, & t cancel)

W = 20*5*7*4 / 4*2*5*2 (rewrite after cancellation)

W = 35 (perform the division from above)