AP ICET 2016 Paper

Question : 10 of 200

Marks: +1, -0

What is the length of the side BC in the triangle ABC?
I.

AB=8cm,AC=5cm

II. Area of the triangle ABC is

10cm^2

if the statement 1 alone is sufficient to answer the question.
if the statement II alone is sufficient to answer the question.
if both the statements I and II are sufficient to answer the question but neither statement alone is sufficient.
if both the statements I and II together are not sufficient to answer the question and additional data is required.

Validate

Solution:

I. Given : AB = 8 cm, AC = 5 cm
It is not possible to determine BC. We need one more information like ∠BAC or area ΔABC or perimeter of the triangle.
∴ I alone is not sufficient.
II. Given : Area of ΔABC = 10 cm2
II alone is not sufficient.
I & II.
Using Heron’s formula, area of the triangle is given by

√{s(s-a)(s-b)(s-c)}

where

s={a+b+c}/2

We have ‘b’ and ‘c’ from statement I and area from statement II.
Hence, ‘a’ i.e., BC can be determined using this relation.
∴ I & II together are sufficient.

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