The width of a square-based storage tank is 3m less than its height. The tank has a capacity of 20 m3. If the dimensions are integer values in metres, what are they?

Question

anonymous · Answer

Let h denote the height, so the width is h-3.
Volume = h(h-3)² = 20
h(h²-6h+9) = 20
h³-6h²+9h = 20
h³-6h²+9h-20 = 0
(h-5)(h²-h+4) = 0
h-5 = 0
h = 5

The dimensions are 5m by 2m by 2m.

I hope this helps.

anonymous · Answer

how did you get from $$(h-5)(h ^{2}-h+4)=0$$ to (h-5)=0 ?

anonymous · Answer

--->(h-5)<---(h²-h+4) =--->0<---=h-5 = 0

anonymous · Answer

i still don't get it...

anonymous · Answer

because (H-5)(h2-h+4)=0 so we put it together=H-5 so H-5=0 and that's the answer

anonymous · Answer

oh okay thanks

anonymous · Answer

your welcome

anonymous · Answer

I still domt get why h-5. Equals to zero . .