Question

18. A group of boys in a camp wanted to set up a tent. The
slanted sides are both 2.5 metres long and the bottom of
the tent is 3 metres feet across. What is the height of the
tent, in metres, at its tallest point?

Answer 1

Answer:

2 meters

Step-by-step explanation:

the tent will form a cubical sturucture as shown in fig.

given

ac=ab=2.5 meters

 and bc =3 meters

draw a perpendicular from a to bc, it will be also the mid point of bc.

hence, bd=$\frac{bc}{2}$=$\frac{3}{2}$=1.5 meters

according to pythagoras theorem,

$height^{2}=hypotenuse^{2}-width^{2}$

now in right angled triangle abd

$ad^{2} =ab^{2} -bd^{2}$

$ad^{2} =2.5^{2} -1.5^{2}$

$ad^{2}$=4

ad=2 metes

hence the height of its tallest point is 2 meters