The base of right pyramid is an equilateral triangle, each side of which is 20 cm. Each slant edge is 30 cm. The vertical height (in cm) of the pyramid is:

Answer: Option B

Solution

Answer: Option B

Solution:

$$\begin{array}{rl}& \text{Length of eaeh side}=20\text{cm }\\ & \text{Cireumradius}=OC=\frac{a}{\sqrt{3}}=\frac{20}{\sqrt{3}}\\ & \text{Slant edge}=DC=30\text{ cm}\\ & \text{In }\Delta ODC\\ & D{C}^2=O{D}^2+O{C}^2\\ & 30^2=O{D}^2+{\left(\frac{20}{\sqrt{3}}\right)}^2\\ & O{D}^2=900-\frac{400}{3}\\ & OD=\sqrt{\frac{2300}{3}}\\ & OD=10\sqrt{\frac{23}{3}}\end{array}$$