# A right triangle when one side is 3.5 cm and sum of other sides and the hypotenuse is 5.5 cm. Construct the following and give justification

**Solution:**

Consider the __right triangle__ as ABC

It is given that

BC = 3.5 cm

∠B = 90°

AB + AC = 5.5 cm

Steps of Construction

1. Construct the base BC = 3.5 cm

2. Construct ∠XBC = 90° at B of base BC

3. Now cut the line segment BD which is equal to AB + AC = 5.5 cm from XB

4. Join DC and construct an ∠DCY which is equal to ∠BDC

5. Let Y intersect BX at the point A

6. So triangle ABC is the required triangle

Justification

∠B and base BC are drawn

In triangle ACD

∠ACD = ∠ADC (from construction)

As the sides opposite to equal angles are equal

AD = AC …. (1)

From equation (1)

AB = BD - AD = BD - AC

BD = AB + BC

Therefore, the construction is justified.

**✦ Try This: **Construct a right triangle when one side is 4.5 cm and sum of other sides and the hypotenuse is 6.5 cm. Give justification.

**☛ Also Check: **NCERT Solutions for Class 9 Maths Chapter 11

**NCERT Exemplar Class 9 Maths Exercise 11.4 Problem 3**

## A right triangle when one side is 3.5 cm and sum of other sides and the hypotenuse is 5.5 cm. Construct the following and give justification

**Summary:**

A right triangle when one side is 3.5 cm and sum of other sides and the hypotenuse is 5.5 cm is constructed and justified

**☛ Related Questions:**

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