Maths-
General
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) cross times x or y = k cross times 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.
    alpha 1 over h
    b = k over h……(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 cross times 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 = k over 6
    Now, put the value of k = 126
    b = 126 over 6
    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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