Question

M
1.
The length of the sides of a triangle are in the ratio 3:4:5 and its perimeter is 144 cm.
The area of the triangle is:
fol 764 m2 (d) 864 cm​

Answer 1

Answer:

perimiter of a triangle is 144cm.

let the x will be the equal devider of the sides.

then 3x , 4x & 5x will be the sides.

3x + 4x + 5x = 144

12x = 144 x = 144/12 = 12

3x = 3 * 12 = 36

4x = 4* 12 = 48

5x = 5 * 12 = 60

according to hero's formula = √s ( s - a) (s- b) (s- c)

s= perimeter/2 = 144/2 = 72cm

√ 72 * ( 72- 36 ) (72 - 48) ( 72 - 60)

√72( 36) (24) (12)

√ 36 * 2 * 36 * 12 * 2 * 12

36* 12* 2 = 864cm^2 will be area of a triangle.

Answer 2

we know that perimeter of triangle = sum of its sides

therefore let the sides be

3x, 4xand 5x

therefore perimeter will be

3x+4x+5x=144

12x=144

x=12

hence the sides will be

3×12, 4×12, 5×12

vthat is

36,48,60

now the area of triangle will be

by heron's formula

Let a,b,c be the lengths of the sides of a triangle. The area is given by:

Area = √ p ( p − a ) ( p − b ) ( p − c )

where p is the perimeter /2

hence the area will be

a= √{72(72-36)(72-48)(72-60)]

the area of triangle is

864 cm²

this is your required ans

hope it helped

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