Question

the sides of a triangle are in ratio 3:4:5$ ite perimeter is 144cm find the area of triangle

Answer 1

Hii !!

Let sides of triangle are 3X , 4X and 5X.

Perimeter of triangle = 144

3X + 4X + 5X = 144

12X = 144

X = 144/12

X = 12 .

First side = A = 3X = 3 × 12 = 36 cm

Second sides = B = 4X = 4 × 12 = 48 cm.

And,

Third side = C = 5X = 5 × 12 = 60 cm..

Therefore,

Semi Perimeter ( S ) = A + B + C /2 = 144/2 = 72 cm.

Therefore,

( S - A ) = ( 72 - 36 ) = 36 cm

( S - B ) = ( 72 - 48) = 24 cm.

And,

( S - C ) = ( 72 - 60 ) = 12 cm.

So,

Area of triangle = √S - ( S - A ) ( S - B ) ( S - C )

=> √72 × 36 × 24 × 12

= √746496

=> 864 cm².

Hence,

Area of triangle = 864 cm².

Answer 2

Heya mate, Here is ur answer

$\huge\boxed {\red{ \mathfrak{answer}}}$

Let the common ratio be x.

So, the sides are =

3x , 4x and 5x .

A/Q

Sum of three sides(Perimeter) = 144

3x+4x+5x=144

12x=144

x=144/12

x=12

So, the sides are 3×12 =36 cm.

4×12 =48 m

5×12=60 m

s(semiperimeter) =perimeter/2

=144/2

=72 cm

a=36 , b =48 , c=60

$<b><u>Using Heron's formula for finding the area </u></b>$

Area
$= \sqrt{s(s - a)(s - b)(s - c)}$

$= \sqrt{72(72 - 36)(72 - 48)(72 - 60)}$

$= \sqrt{72 \times 36 \times 24 \times 12}$

Factorising each term

$= \sqrt{3 \times 2 \times 3 \times 2×2\times 6 \times 6 \times 2×3 \times 2 \times 2 \times 3 \times 2 \times 2}$

$= 2 \times 2 ×2×2\times 6 \times3×3$

$= 864\: cm {}^{2}$

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@Laughterqueen

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