Question

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$\underline{\texit{Please \: help \: me \: to }}$
$\underline{\texit{ solve \: this \: question}}$

Class : 9

Subject : Maths

Chapter : Heron's Formula

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Answer 1

Let the length of the base be 2b

Heron’s formula:  

Area = √p(p - a)(p - b) (p - c)

Find P:

P = (8 + 8 + 2b) ÷ 2

P = (16 + 2b ) ÷ 2

P = 8 + b


Find area in term of b:

Area = √(8 + b) ( 8 + b - 8) ( 8 + b - 8) ( 8 + b - 2b)

Area = √(8 + b)( b) (b) (8 - b)

Area = √b² (8² - b²)

Find b:

Given that area = 4√15

√b² (8² - b²) = 4√15

b² (8² - b²) = 240

64b² - b⁴ = 240

b⁴ - 64b² + 240 = 0

(b² - 4)(b² - 60) = 0

b² = 4 or b² = 60

b = ±√4 or b = ±√60

b = 2 or -2 or 2√15 or -2√15

b cannot be negative, therefore

b = 2 or 2√15

Find the base:

base = 2b

base = 2(2) or 2(2√15)

base = 4 or 4√15

Answer: The base is  4 cm or 4√15 cm