The picture shows a sandwich box: a sandwich box is shown with a right triangle side. the right triangle has hypotenuse 9 cm and base 6 cm. what is the approximate minimum height of a shelf in which this box can fit in the position shown in the picture? 3 centimeters 6.7 centimeters 7.5 centimeters 8 centimeters

Solution:

In right triangle depicted in the diagram

Hypotenuse = 9 cm

Base = 6 cm

As we know ,By pythagoras theorem

(Hypotenuse)²= (Base)² + (Altitude)²

⇒9²= 6² + (Altitude)²

⇒81 - 36= (Altitude)²

⇒ (Altitude)²= 45

⇒ Altitude = √45= cm

So, Altitude = 5 × 1.732=    8.660 cm

So, Approximate minimum height of shelf so that box can fit in the picture described = 8 centimeters  

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