Question

the length of a sides of a triangle are in the ratio 3:4:5& its perimeter is 144cm. the area of the triangle is​

Answer 1

The area of triangle is 864 cm² and the height corresponding to the longest side is 28.8 cm.

Step-by-step explanation:

The length of the sides of a triangle are in the ratio 3:4:5. Let the length of sides be 3x,4x,5x.

It is given that the perimeter of the triangle is 144 cm.

$3x + 4x + 5x = 144$

$12x = 144$

$= 12$

The value of x is 12. It means the length of sides are 36,48,60.

Using heron's formula the area of triangle is

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

Where,

$s = \frac{a + b + c}{2}$

$s = \frac{144}{2} = 72$

The area of triangle is

$\sqrt{72 } (72 - 36)(72 - 48)(72 - 60) = 864$

The area of triangle is 864 cm².

The area of triangle is

$a = \frac{1}{2} \times b \times h$

$864 = \frac{1}{2} \times 60 \times h$

$height = \frac{864}{3} = 288$

The height corresponding to the longest side is 288 cm

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Answer 2

hi mate,

answer :The area of triangle is 864 cm² and the height corresponding to the longest side is 28.8 cm.

Step-by-step explanation:

The length of the sides of a triangle are in the ratio 3:4:5. Let the length of sides be 3x,4x,5x.

It is given that the perimeter of the triangle is 144 cm.

Let

the side = 3 x 4 x 5 x

144 = 3x + 4 x + 5 x

x = 144 / 12

x = 12

now we multiply by

3* 12 = 36 Cm = a

4* 12=48cm = b

5* 12=60cm = c = base....

S = a+b+c/2

36 + 48 + 60/2

144/2 = 72

triangle area = √ s (s - a) (s-b) ( s-c)

triangle area

= √ 72 (72-36) (72-48) (72-60)

triangle area = √72 (36) (24) (12)

triangle area = √746496

triangle area=864cm²

triangle area = ½ * base * height

864 = ½* 60 *height

864 = 30 *height

height = 864/30 = 28.8 cm

The height corresponding to the longest side is 28.8 cm.

i hope it helps you.....

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