The two sides of a triangle are 3 cm and 5 cm. What is the maximum possible length of the third side of the triangle?a) 2b) 5c) 7d) 6
Given :
The two sides of a triangle are 3 cm and 5 cm.
To do:
We have to find the maximum possible length of the third side of the triangle.
Solution:
Let the length of the third side be 'a' cm.
The lengths of the three sides of the triangle are 3 cm, 5 cm, and a cm.
The triangle inequality rule states that the sum of two sides of a triangle is greater than the third side.
Therefore,
$3 cm + 5 cm > a cm$
$8 cm > a cm$
From the given options, the maximum length of the third side is 7 cm.
Option (c) is correct.
Related Articles
- Two sides of a triangle are \( 12 \mathrm{~cm} \) and \( 14 \mathrm{~cm} \). The perimeter of the triangle is \( 36 \mathrm{~cm} \). What is the length of the third side?
- The length of two sides of a triangle are \( 4 \mathrm{~cm} \) and \( 6 \mathrm{~cm} \). Between what two measurements should the length of the third side fall?
- Two sides of a triangle are \( 12 \mathrm{~cm} \) and \( 14 \mathrm{~cm} \). The perimeter of the triangle is \( 36 \mathrm{~cm} \). What is its third side?
- The lengths of two sides of a triangle are 12 cm and 15 cm. Between what two measures should the length of the third side fall?
- If two sides of a right triangle are 3 cm and 7 cm. What is the length of the hypotenuse?
- Construct a triangle of sides 4 cm, 5 cm and 6 cm and then a triangle similar to it whose sides are $\frac{2}{3}$ of the corresponding sides of the first triangle.
- If the sides of a triangle are 3 cm, 4 cm, and 6 cm long, determine whether the triangle is a right-angled triangle.
- Construct a triangle with sides 5 cm, 6 cm and 7 cm and then another triangle whose sides are $\frac{7}{5}$ of the corresponding sides of the first triangle.
- The two sides of a right-angled triangle are 6 cm and 8 cm. Find the length of the hypotenuse.
- Find the perimeter of each of the following shapes :(a) A triangle of sides \( 3 \mathrm{~cm}, 4 \mathrm{~cm} \) and \( 5 \mathrm{~cm} \).(b) An equilateral triangle of side \( 9 \mathrm{~cm} \).(c) An isosceles triangle with equal sides \( 8 \mathrm{~cm} \) each and third side \( 6 \mathrm{~cm} \).
- The difference between the two adjoining sides of a triangle is \( 20 \mathrm{~cm} \), third side is \( 40 \mathrm{~cm} \) and the perimeter of the same triangle \( 120 \mathrm{~cm} \). Find the area of the triangle.
- Draw a triangle ABC with side $BC = 6\ cm, AB = 5\ cm$ and $∠ABC = 60^o$. Then construct a triangle whose sides are $\frac{3}{4}$ of the corresponding sides of the triangle $ABC$.
- The hypotenuse of a right-angled triangle is 25 CM if one of the remaining two sides is 24 cm find the length of its third side.
- Construct a triangle with sides \( 5 \mathrm{~cm}, 6 \mathrm{~cm} \) and \( 7 \mathrm{~cm} \) and then another triangle whose sides are \( \frac{5}{7} \) of the corresponding sides of the first triangle.
- Areas of two similar triangles are $36\ cm^2$ and $100\ cm^2$. If the length of a side of the larger triangle is $3\ cm$, then find the length of the corresponding side of the smaller triangle.
Kickstart Your Career
Get certified by completing the course
Get Started