The sides of a triangle are 16 cm, 12 cm and 20 cm. Find : (i) area of the triangle (ii) height of the triangle, corresponding to the largest side
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Answer:
Sides of triangle a=12cm, b=16cm and c=20cm
s=
2
a+b+c
=
2
12+16+20
=
2
48
=24cm
Using Heron's formula,
Area of a triangle=
s(s−a)(s−b)(s−c)
=
(24−12)(24−16)(24−20)
=
(12)(8)(4)
=
4×3×4×3×4
=4×3×2=24sq.cm
AD is height of ∆ corresponding to largest side.
∴ (1/2) × BC × AD = 96
(1/2) × 20 × AD = 96
AD = (96 × 2)/20
AD = 9.6 cm
BE is height of ∆ corresponding to smallest side.
(1/2) AC × BE = 96
(1/2) × 12 × BE = 96
BE = (96 × 2)/12
BE = 16 cm
(i) 96 cm2 (ii) 9.6cm (iii) 16cm
Step-by-step explanation:
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