Question

The length of the sides of a triangle are in the ratio 2:3::4and its perimeter is 144 cm. Find the area of the triagnle and the height corresponding to the longest side.

Answer 1

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sol:

Sides of triangle are: a = 3k, b = 4k, c = 5k

Perimeter of triangle = a + b + c = 144(Given)

=> 3k + 4k + 5k = 12k = 144

=> k = 12

Sides are: 36 unit, 48 unit, 60 unit

S = (a + b + c )/2 = (36 + 48 + 60)/2 = 72

Area of triangle = √s(s-a)(s-b)(s-c) = √72×36×24×12 = 864 unit^2

Now, Area of triangle considering the longest side as base: 1/2 × base × altitude(or height)

=> 864 = 1/2 × 60 × altitude

=> altitude = 864/30 = 28.8 unit

Thus, the corresponding Altitude to the longest side is 28.8 unit.

Hope it helps you !

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Answer 2

Answer :-

The area of triangle is 642.1444055cm² and the height corresponding to the longest side is 19.94237284 cm.

Step-by-step explanation:

The length of the sides of a triangle are in the ratio 2:4:5. Let the length of sides be 2x,4x,5x.

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

Let

the side = 2x, 4x, 5x

144 = 2x + 4 x + 5 x

x = 144 / 11

x = 13.09090909 approximately

x = 13

so, now we multiply by

2×13 = 26cm = a

4×13=52cm = b

5×13=65cm = c = base....

S = (a+b+c)/2

(26 + 52 + 65)/2

143/2 = 71.5

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

triangle area

= √ 71.5 (71.5-26) (71.5-52) (71.5-65)

triangle area

= √71.5 (45.5) (19.5) (6.5)

triangle area = √412349.4375

triangle area= 642.1444055 cm²

triangle area = ½ * base * height

642.1444055= ½* 65 *height

642.1444055= 32.5 *height

height = (642.1444055 ) /32.5

= 19.94237284 cm

The height corresponding to the longest side is 19.94237284cm.

i hope it helps you..