# Construct a triangle with sides 4 cm, 5 cm, and 6 cm.

**Given :**

The given sides of the triangle are 4 cm, 5 cm, and 6 cm.

**To do :**

We have to construct a triangle with given sides.

**Solution :**

**Construction of a triangle :**

To construct a triangle when the lengths of all three sides are given, we need the a

Ruler and a Compass

**Example :
**

Construct a triangle $ABC$ given that $AB = 4cm, BC = 6 cm$ and $AC = 5 cm$.

**Step 1 :
**

Draw a line segment $BC = 6cm$.

**Step 2 :
**

With ‘$B$’ as the center, draw an arc of radius $4 cm$ above the line $BC$.

**Step 3 :**

With ‘$C$’ as the center, draw an arc of $5 cm$ to intersect the previous arc at ‘$A$’.

**Step 4 :**

Join $AB$ and $AC$. Now $ABC$ is the required triangle.

- Related Articles
- 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.
- 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.
- 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.
- Construct a triangle with sides \( 5 \mathrm{~cm}, 5.5 \mathrm{~cm} \) and \( 6.5 \mathrm{~cm} \). Now, construct another triangle whose sides are \( 3 / 5 \) times the corresponding sides of the given triangle.
- Construct a triangle $ABC$ such that $BC = 6\ cm, AB = 6\ cm$ and median $AD = 4\ cm$.
- Construct a triangle of sides \( 4 \mathrm{~cm}, 5 \mathrm{~cm} \) and \( 6 \mathrm{~cm} \) and then a triangle similar to it whose sides are \( (2 / 3) \) of the corresponding sides of it.
- Is it possible to have a triangle with the following sides?$(i).\ 2 cm,\ 3 cm,\ 5 cm$$(ii).\ 3 cm,\ 6 cm,\ 7 cm$$(iii).\ 6 cm,\ 3 cm,\ 2 cm$
- 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 $ABC$.
- Draw a triangle ABC with $BC = 6\ cm, AB = 5\ cm$ and $\vartriangle ABC=60^{o}$. Then construct a triangle whose sides are $\frac{3}{4}$ of the corresponding sides of the ABC.
- If the sides of a triangle are 3 cm, 4 cm, and 6 cm long, determine whether the triangle is a right-angled triangle.
- 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 \( 6 \mathrm{~cm} \).
- Construct a $\vartriangle ABC$ in which $CA= 6\ cm$, $AB= 5\ cm$ and $\angle BAC= 45^{o}$, Then construct a triangle whose sides are $\frac {3}{5}$ of the corresponding sides of ABC.
- Construct $âˆ†XYZ$ in which $XY=4.5\ cm,\ YZ=5\ cm$ and $ZX=6\ cm$.
- Find the perimeter of a triangle having sides of length 5.5 cm and 6 cm and 6.5 cm.
- Is the triangle with sides \( 25 \mathrm{~cm}, 5 \mathrm{~cm} \) and \( 24 \mathrm{~cm} \) a right triangle? Give reasons for your answer.

##### Kickstart Your Career

Get certified by completing the course

Get Started