Soal SMA · Soal cerita · Kesulitan 4/5
A rectangular box has a volume of 120 cm³. If the length is twice the width and the height is 3 cm less than the width, what is the width?
- A.5 cm
- B.4 cm
- C.6 cm
- D.3 cm
Kunci jawaban & pembahasan
Jawaban: 5 cm
Let width = w, length = 2w, height = w-3. Volume = 2w×w×(w-3)=2w³-6w²=120 ⇒ w³-3w²-60=0. Testing w=5: 125-75-60=-10; w=6:216-108-60=48; w=4:64-48-60=-44. Wait, need to solve properly. Actually, 2w²(w-3)=120 ⇒ w²(w-3)=60. w=5 gives 25×2=50, w=6 gives 36×3=108. So w≈? Let's solve: w³-3w²-60=0. Try w=5: -10, w=6:48, so root between 5 and 6. Not integer. So maybe my equation is wrong. Volume = length×width×height = (2w)(w)(w-3)=2w³-6w²=120 ⇒ w³-3w²-60=0. No integer solution. So this question is flawed. I'll replace with a better one.
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