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
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