Direction: Each of the questions below consists of a question and three statements numbered I, II and III given below it. You have to study the questions and decide the data in which of the statements are sufficient to answer the questions.
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What is the area of the isosceles triangle?
I. Perimeter of the triangle is 14 m.
II. Base of the triangle is 14 m.
III. Height of the triangle is 5 m.
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- I and II only
- II and III only
- I and II only or, II and III only
- I and III only
- All I, II and III
Correct Option: B
According to question ,
I. Perimeter of the triangle ( 2s )= a + b + c = 14 where, b = c
⇒ a + b + b = 14 ⇒ a + 2b = 14
II. Base of the triangle ( a ) = 14 cm
III. Height of the triangle ( h ) = 5 cm
From II and I , we have
⇒ 14 + 2b = 14 ⇒ 2b = 0 ⇒ b = 0 = c
Now , we find
| Required area of triangle = | 1 | x base x height |
| 2 |
| The area of triangle = | 1 | x 14 x 5 = 35 cm2 |
| 2 |
So, by combining I and II, we are getting the values of b and c as zero, which is not possible. So, only by combing II and III we get the value of the area, which is equal to 35 cm2.
