Question

The sides of a triangle are in the ratio 3:5:6. If the perimeter of the triangle is 24 cm, find the length of each side.

Answer 1

Answer:

Let a and b be the sides and c the hypotenuse.

c2=a2+b2…..(1)

a+b+c=24……….(2)

ab2=24i.e.ab=48……..(3)

c2=(a+b)2–2ab=(24−c)2–96

(24−c)2−c2=96

(24−c+c)(24−c−c)=96

c=10

a+b=14

a−b=(a+b)2–2ab−−−−−−−−−−√=100–96−−−−−−√=2

from these two a=8 and b=6

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Step-by-step explanation:

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Answer 2

$\huge\mathfrak\pink{Answer}$

Let a and b be the sides and c the hypotenuse.

c2=a2+b2.(1)

a+b+c=24(2)

ab2=24i.e.ab=48(3)

c2=(a+b)2–2ab=(24−c)2–96

(24−c)2−c2=96

(24−c+c)(24−c−c)=96

c=10

a+b=14

a−b=(a+b)2–2ab−−−−−−−−−−√=100–96−−−−−−√=2

from these two a=8 and b=6