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Q1. Can we form a triangle having angles 58o , 80o and 90o ?

Solution

No comma space we space can space not space form space straight a space triangle space having space angles space 58 degree comma space 80 degree space and space 90 degree. As space space 58 degree space plus space 80 degree space plus space space 90 degree space equals space 228 degree space. This space contradicts space to space apostrophe sum space of space measures space of space all space the space angles space of space straight a space tiangle space is space 180 degree apostrophe.
Q2. Answer what kind of triangle it is: (a) A triangle has angle measurements of 90o, 20o and 70o? (b) A triangle has angle measurements of 14o, 30o and 136o? (c) A triangle has angle measurements of 76o, 68o and 36o?

Solution

We know that In an acute-angled triangle, all three angles are less than 90°. In a right-angled triangle, one angle is exactly 90o. In an obtuse-angled triangle, one angle is greater than 90o. (a) This triangle is a right-angled triangle because it has a 90o angle which is a right angle. (b) This triangle is an obtuse-angled triangle because it has a 136o angle which is an obtuse angle. (c) This triangle is an acute-angled triangle because it has all three angles acute, that is less than 90o.
Q3. Is it possible to have a triangle with the sides having following lengths? 5 cm, 3 cm, 4 cm

Solution

We know that the sum of two sides of a triangle is always greater than the third. The given lengths of the sides are 5 cm, 3 cm, 4 cm. Let us check whether the above stated property holds true. We have: 5 + 3 = 8, which is greater than 4 5 + 4 = 9, which is greater than 3 3 + 4 = 7, which is greater than 5 Thus, it is possible to draw a triangle with given side lengths.
Q4. Will a median always lie in the interior of a triangle?

Solution

Median of a triangle is the line joining the vertex to the midpoint of the side opposite to it. So a median will always lie in the interior of a triangle.
Q5. Determine whether the triangle whose lengths of sides are 5 cm, 12 cm and 13 cm is a right-angled triangle.

Solution

In any right-triangle, the hypotenuse happens to be the longest side. Thus, we have to check h2 = p2 + b2 Here, 52 = 5 x 5 = 25; 122 = 12 x 12 = 144 and 132 = 13 x 13 = 169 So we find, 52 + 122 = 25 + 144 = 169 = 132 Therefore, the triangle is right-angled.
Q6.  A right triangle has side with length of 7 cm and length of hypotenuse is 25 cm,find the length of other side?

Solution

Let space the space other space side space is space straight x space cm. In space straight a space right space angle space triangle comma open parentheses Hypotenuse close parentheses squared equals space sum space of space the space squares space of space other space two space sides 25 squared space equals space 7 squared space plus space x squared 625 minus 49 space equals space x squared x squared space equals space 576 x space equals space 24 space cm Length space of space the space other space side space is space 24 space cm.
Q7.  A triangle has sides with lengths of 5 cm, 13 cm  and 12 cm, then can we say that the triangle is right triangle?

Solution

For space straight a space triangle space to space straight a space right space triangle space it space should space satisfy space the space pythagoras space theorem. That space is comma open parentheses Hypotenuse close parentheses squared equals space sum space of space the space squares space of space other space two space sides Given space triangle space has space sides space with space lengths space of space 5 space cm comma space 13 space cm space space and space 12 space cm. 12 squared plus 5 squared space equals 144 space plus space 25 space equals 169 space equals space 13 squared So space given space triangle space satisfies space space pythagoras space theorem. Hence space space we space can space say space that space straight a space triangle space having space sides space with space lengths space of space 5 space cm comma space 13 space cm space space and space 12 space cm comma space is space space straight a space right space triangle.
Q8. Define the property for lengths of sides of the triangle. Using it, state whether a triangle is possible with sides: 10.7 cm, 5.6 cm and 3.5 cm.

Solution

The property of sides of triangle states that: "Sum of the lengths of any two sides of a triangle is greater than the length of the third side." Now, The sides of a triangle are given as 10.7 cm, 5.6 cm, 3.5 cm Suppose such a triangle is possible. Then the above property can be applicable. Let us check that. 10.7 + 5.6 = 16.3, which is greater than 3.5 5.6 + 3.5 = 9.1, which is less than 10.7 Thus the property is not satisfied. Hence, the triangle is not possible.
Q9. Is it possible to have a triangle with the following sides? 2 cm, 9 cm, 6 cm

Solution

We know that the sum of two sides of a triangle is always greater than the third. The sides of a triangle are given as 2 cm, 9 cm, 6 cm Suppose such a triangle is possible. Then the above property will be applicable. Let us check that. 2 + 9 = 11, which is greater than 6 9 + 6 = 15, which is greater than 2 2 + 6 = 8, which is less than 9 Thus, the triangle is not possible.
Q10. The lengths of two sides of a triangle are 11 cm and 14 cm. Between what two measures should the length of the third side fall?

Solution

We know that the sum of two sides of a triangle is always greater than the third. Therefore, third side has to be less than the sum of the two sides. The third side is thus, less than 14 + 11 = 25 cm. The side cannot be less than the difference of the two sides. Thus, the third side has to be more than 14 - 11 = 3 cm. So, the length of the third side could be any length greater than 3 cm and less than 25 cm.


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