Question
Construct the following and give justification: A right triangle when one side is $3.5\ cm$ and sum of other sides and the hypotenuse is 5$.5\ cm.$
✓
Answer
In $\triangle ABC$, base $BC =3.5 cm$, the sum of other side and hypotenuse i.e., $AB + AC =5.5 cm$ and $\angle ABC =90^{\circ}$ To construct, An $\triangle ABC$. Steps of construction,
1. Draw a ray $B X$ and cut off a line segment $B C=3.5 cm$ from it.
2. Construct $\angle XBY =90^{\circ}$ with the help of a ruler and compass.
3. From by cut off a line segment $B D=5.5 cm$.
4. Join $CD.$
5. Draw the perpendicular bisector of $C D$ intersecting $B D$ at $A$.
6. Join $A C$. Then, $A B C$ is the required triangle.
1. Draw a ray $B X$ and cut off a line segment $B C=3.5 cm$ from it.
2. Construct $\angle XBY =90^{\circ}$ with the help of a ruler and compass.
3. From by cut off a line segment $B D=5.5 cm$.
4. Join $CD.$
5. Draw the perpendicular bisector of $C D$ intersecting $B D$ at $A$.
6. Join $A C$. Then, $A B C$ is the required triangle.
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