Triangles Test

Result

Triangles Test - 5

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Weekly Quiz Competition

Question 1
1 / -0

The side lengths of a degenerate triangle ΔABC are 4, 11 and c. Which of the following is correct?

A
7 < c < 15

B
11 < c < 15

C
4 < c < 11

D
4 < c < 7

Solution

Theorem: The sum of lengths of two sides is always greater than the third side.

Therefore,

4 + 11 > c

15 > c

c < 15

Also,

4 + c > 11

c > 11 – 4

c > 7

And,

11 + c > 4

c > 4 – 11

c > -7

But negative side is not possible.

Therefore,

7 < c < 15

Hence, A is the correct answer.
Question 2
1 / -0

Two legs of an isosceles triangle have length 12 and 27 respectively. What is the perimeter of the triangle?

A
66

B
78

C
51

D
72

Solution

In an isosceles triangle, two sides are equal.

Given two sides are 12 and 27.

Let 12 be the side that is equal,

Then, the sides of the triangle are 12, 12, and 27

Theorem: The sum of two sides is always greater than the third side.

12 + 12 < 27
24 < 27

Therefore, 12 cannot be the side that is equal.

When, 27 is the side that is equal,

Then, the sides of the triangle are 12, 27, and 27

12 + 27 > 27 [Possible]

Perimeter = 12 + 27 + 27 = 66

Hence, A is the correct answer.
Question 3
1 / -0

If AB = 8cm, BC = 15cm, and CA = 19cm then which of the following is correct?

A
ABC is a scalene triangle.

B
ABC is an isosceles triangle.

C
ABC is a right-angled triangle.

D
Triangle of sides A, B, and C is not possible.

Solution

Theorem: The sum of any two sides of a triangle is greater than the third side.

Given: AB = 8cm, BC = 15cm, and CA = 19cm

AB + BC > CA

AB + CA > BC

BC + CA > AB

Therefore, in each case the theorem is valid.

The sides are of unequal length.

Therefore, sides AB, BC, and CA form a scalene triangle.

Hence, A is the correct answer.
Question 4
1 / -0

A triangle ABC have side lengths AB = a cm, BC = 17 cm and AC = 12 cm then which of the following is correct range for AB?

A
12 < a < 17

B
12 < a < 29

C
5 < a < 17

D
5 < a < 29

Solution

Theorem: The sum of any two sides of a triangle is greater than the third side.

Now, a + 17 > 12, a > 12 – 17, a > -5 [But negative lengths are not possible.

a + 12 > 17

a > 17 – 12

a > 5

Also,

12 + 17 > a

29 > a

a < 29

Therefore,

a > 5 and a < 29

Hence, D is the correct answer.