Question

The lengths og the sides of the triangle are in the ratio 3:4:5 and its perimeter is 144cm. find the area of the triangle and the height corresponding to the longest side

Answer 1

Let the sides are a = 3x b = 4x c = 5x

3x + 4x + 5x = 144

x = 144/12 = 12

a = 12×3 = 36

b = 12×4 = 48

c = 12 × 5 = 60


$s = a + b + c \div 2$

$s = 144 \div 2 = 72$

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

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

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

$\sqrt{6 \times 3 \times 4 \times 6 \times 6 \times 4 \times 6 \times 2 \times 6}$

$6 \times 6 \times 4 \times 3 \times 2$

$area \: = 864$

Longest side = 60

Area of Triangle = 1/2 × b × h

864 = 1/2 × 60 × h

(864 × 2) / 60 = h

h = 28.8


Thanks

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..