Question

A right pyramid stands on a rectangular base whose sides are 24 cm and 18 cm and each of the slant edges is 17 cm. The height of the pyramid is

• A. 8 cm
• B. 10 cm
• C. 12 cm
• D. 15 cm

Answer 1

The correct option is A 8 cm

AB = Dc = 24 cm
BC = AD = 18 cm
and each slant height = OA = OB = O = OD = 17 cm
OX is the perpendicular such that $\angle OXB={90}^{\circ }$ and X is the mid point of the base, XB = XD = $\frac{1}{2}BD$
OX = height = h = $\sqrt{O{B}^2-X{B}^2}$
= $\sqrt{{17}^2-(\frac{BD}{2}{)}^2}$ ($B{D}^2=A{B}^2+B{C}^2$= ${24}^2+{18}^2$ = 900)
= $\sqrt{{17}^2-\frac{900}{4}}$
= 8 cm