The length of the base of a triangle with a constant area varies inversely as the height. When the base is 18 cm long, the height is 7 cm. Find the length of the base when the height is 6 cm

The correct answer is: 21 cm

Let the length of the base be represented as b and the height of the triangle be represented as h. We are given that the length of the base of a triangle with a constant area varies inversely as the height.
b  
b = ……(1)
where k is a proportionality constant
Step 1 of 2:
It is given that when the base is 18 cm long, the height is 7 cm i.e. b = 18 and h = 7. Putting the values in equation (1)
18 =
k = 18  7  = 126
Step 2 of 2:
Now we are asked to determine the length of the base if the height is 6 cm. So, h = 6 and we need to find b. Putting the values in equation (1)
b = 
Now, put the value of k = 126
b = 
b = 21 cm
Final Answer:
Hence, the length of the base is 21 cm if the height is 6 cm
Note: We can also solve this by equating the area of the triangle in both cases.