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 1

In the right triangle ABC, given BC = 3.5 cm, ∠B = 90° and sum of other side and hypotenuse be, AB + AC = 5.5 cm

To construct a triangle ABC use the following steps:

1. Draw the base BC = 3.5 cm

2. Make an angle XBC = 90° at the point B of base BC.

3. Cut the line segment BD equal to AB + AC i.e., 5.5 cm from the ray XB.

4. Join DC and make an ∠DCY equal to ∠BDC.

5. Let Y intersect BX at A. Therefore, ABC is the required triangle.

Justification:

Base BC and ∠B are drawn as given.

In ΔACD, ∠ACD = ∠ADC  ...[By construction]

AD = AC  ...(i) [Sides opposite to equal angles are equal]

Now, AB = BD – AD = BD – AC  ...[From equation (i)]

BD = AB + AC

Hence, our construction is justified.