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Question

Draw a triangle with sides 5 cm, 6 cm and 6 cm. Draw a square having the same area as the triangle.

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Solution

(A)
Steps of Construction for triangle:
1. Draw a line segment BC of length 5cm.
2. Measure distance of 6 cm in compass. Taking B as centre draw an arc.
3. Taking C as centre with same distance and draw another arc.
4. Both the arcs intersect each other; name that point of intersection as A.
5. Required triangle ABC is drawn.
Area of ΔABC can be calculated using Heron's formula.

s=5+6+62

=172cm

Therefore, Area ABC=172(1725)(1726)(1726)

=172×72×52×52

=13.6cm2

Therefore, Area of Square =(side)2

13.63=(side)2

side=3.7cm

(B)
Now, Steps of Construction for square:

1.Draw segment BC of length 3.7cm.
2.Draw a line perpendicular to BC through B.
Measure a distance of 3.7 cm in compass and cut this line at point A.
3.Draw a line perpendicular to BC through C.
Measure a distance of 3.7 cm in compass and cut this line at point D.
4.Join AB, CD, and AD.
5.Required square ABCD is drawn.

665089_628188_ans_a8ac877b7cba42ce86423a5fc0e7710c.png

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