Question

if the semiperimeter of a triangle is 96, and the ratio of its sides are 3:4:5, what is the area of the triangle

Answer 1

Answer:

refer to the attachment

Answer 2

Step-by-step explanation:

Let t

be some integer value. sides are in the ratio 3:4:5

.

Now include the ratio value to t

.

Consider the sides assuming that 3t,4t,5t

.

Used Heron's formula,

A=S(S−a)(S−b)(S−c)−−−−−−−−−−−−−−−−−−√

A=S(S−a)(S−b)(S−c)−−−−−−−−−−−−−−−−−−√

S

denoted by a semi-perimeter of the triangle.

Semi-perimeter of triangle =(sum of the sides of triangle)2

Sum of the sides of the triangle =a+b+c

Here a=3t,b=4t,c=5t

96=3t+4t+5t2

192=12t

t=19212

t=16

So that now substitute t

value in a,b

and c

a=3(16)

=48cm

b=4(16)

=64cm

c=5(16)

=80cm

Now apply S,a,b

and c

values in Heron's area formula

Area of triangle =S(S−a)(S−b)(S−c)−−−−−−−−−−−−−−−−−−√

Area of triangle =96(96−48)(96−64)(96−80)−−−−−−−−−−−−−−−−−−−−−−−−√

=96(48)(32)(16)−−−−−−−−−−−−√

Now used prime factorization method,

The prime factorization method means writing the number as the product of its prime factors.

Find the prime factors of 96,48,32,16

Prime factors of,

96=2×2×2×2×2×3−−−−−−−−−−−−−−−−−√

48=2×2×2×2×3−−−−−−−−−−−−−−√

32=2×2×2×2×2−−−−−−−−−−−−−−√

16=2×2×2×2−−−−−−−−−−−√

=2×2×2×2×2×3×2×2×2×2×3×2×2×2×2×2×2×2×2×2−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−√

Take square root,

=2×2×2×2×2×2×2×2×2×3

Product the values,

=1536

This is finding the area sum so we included the cm2

in the final answer.

So that area is 1536cm2