Question 27

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Jambmaths question: 

A frustum of pyramid with square base has its upper and lower section as squares of sizes 2m and 5m respectively and the distance between them 6m. Find the height of the pyramid from which the frustum was obtained.

Option A: 

8.0m

Option B: 

8.4m

Option C: 

9.0m

Option D: 

10.0m

Jamb Maths Solution: 

$\begin{align}  & AC=\sqrt{{{5}^{2}}+{{5}^{2}}}=5\sqrt{2}, \\ & \therefore \text{ }AI=\frac{5\sqrt{2}}{2} \\ & DF=\sqrt{{{2}^{2}}+{{2}^{2}}}=2\sqrt{2} \\ & DH=\frac{2\sqrt{2}}{2}=\sqrt{2} \\ & \text{Using similar triangle} \\ & \frac{x}{\sqrt{2}}=\frac{x+6}{\tfrac{5\sqrt{2}}{2}} \\ & \frac{x}{\sqrt{2}}=\frac{2(x+6)}{5\sqrt{2}} \\ & 5x=2(x+6) \\ & 5x=2x+12 \\ & 3x=12 \\ & x=4 \\ & \therefore \text{The height of the pymaid is (}x+6)cm=(4+6)cm \\\end{align}$

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