Maths-

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Easy

Question

# 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

Hint:

**Hint:**

In a proportional relationship, the variables are related by a constant ratio(k). For example, the equation which can relate the two variables can be written in the form:

y = (constant) x or y = k x.

So, for solving these types of questions we need to create a proportional relationship between the variables. These relationships can be direct, inverse etc.

## 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.

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