Construct ∆ABC such that AB = 2.5 cm, BC = 6 cm and AC = 6.5 cm. Measure ∠B

Solution:

We use the basic rules of construction to solve the question given. We will use scale and compass to do the construction required.

We will draw a rough sketch of ΔABC with the given measures for our reference. This will help us in deciding how to proceed. Then follow the steps given below.

Steps of construction -

1. Draw a line segment BC of length 6cm.
2. From B, we need a point A is at a distance of 2.5cm. So, with B as center, draw an arc of radius 2.5cm. (now A will be somewhere on this arc and our job is to find where exactly A is).
3. From C, point A is at a distance of 6.5cm. So, with C as the center, draw an arc of radius 6.5cm. (now A will be somewhere on this arc, we have to fix it).
4. A has to be on both the arcs drawn, so it is the point of intersection of arcs. Mark the point of intersection of the arcs as A.
5. Join AB and AC.
6. Thus, ABC is the required triangle.
7. Measure angle B with the help of a protractor. It is a right-angled triangle ABC, where ∠B = 90^∘.

☛ Check: NCERT Solutions Class 7 Maths Chapter 10

Video Solution:

Construct ∆ABC such that AB = 2.5 cm, BC = 6 cm and AC = 6.5 cm. Measure ∠B

Class 7 Maths NCERT Solutions Chapter 10 Exercise 10.2 Question 4

Summary:

∆ABC is constructed such that AB = 2.5 cm, BC = 6 cm and AC = 6.5 cm. The value of ∠B = 90^∘.

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