Case Study Based Question on Heron's Formula
While selling clothes for making flags, a shopkeeper claims to sell each piece of cloth in the shape of an equilateral triangle of each side 10 cm while actually he was selling the same in the shape of an isosceles triangle with sides 10 cm, 10 cm and 8 cm. [Use √3=1.73 and √21 = 4.56]
(i) Find the area of an equilateral triangular flag. [1 Mark]
(ii) What is the semi-perimeter of an isosceles triangular Flag. [1 Mark]
(iii) How much cloth was he saving in selling each isosceles flag instead of equilateral flag? [2 Marks]
OR
(iv) What is the altitude of the isosceles triangle with respect to its smallest side? [2 Marks].
Doubt by Veer
Solution :
(i) Find the area of an equilateral triangular flag.
Ans :
a = 10 cm
Area= √3a²/4
=√3×(10)²/4
= √3×100/4
= √3×25
= 25√3
= 25×1.73
=43.25 cm²
(ii) What is the semi-perimeter of an isosceles triangular Flag.
Ans :
a=10 cm
b=10 cm
c=8 cm
s=(a+b+c)/2
s=(10+10+8)/2
s=28/2
s=14 cm
(iii) How much cloth was he saving in selling each isosceles flag instead of equilateral flag?
Ans :
a=10 cm
b=10 cm
c=8 cm
s=14 cm
Using Heron's Formula
Area of isosceles Flag
=√[s(s-a)(s-b)(s-c)]
=√[14(14-10)(14-10)(14-8)]
=√[14(4)(4)(6)]
=√[7×2×4×4×2×3]
=4×2√21
=8√21 cm²
=8×4.56
=36.48 cm²
Area of cloth the shopkeeper was saving in selling each isosceles flag instead of equilateral flag
= 43.25-36.48
= 6.77 cm²
OR
(iv) What is the altitude of the isosceles triangle with respect to its smallest side?
Ans :
Area = 8√21 cm²
Base = 8 cm
Area = ½×Base×Height
2Area/Base = Height
Height = 2Area/Base
=[2×8√21]/8
=2√21
=2×4.56
=9.12 cm