Q14. The length of the sides of a triangle are in the ratio 2 : 3 : 4 and its perimeter is 144 cm. Find: (i) The area of the triangle and (ii) The height corresponding to the longest side. Hurry!!
Answers
Answer:
Step-by-step explanation:
Ratio of lengths=2:3:4
Let the common factor be x
So,
2x,3x,4x
Perimeter=144
2x+3x+4x=144
9x=144
X=144/9
x=16
Answer :-
The area of triangle is 743.6128025cm² and the height corresponding to the longest side is 23.23790008cm.
Step-by-step explanation:-
The length of the sides of a triangle are in the ratio 2:3:4. Let the length of sides be 2x,3x,4x,
It is given that the perimeter of the triangle is 144 cm.
Let,
sides are 2x, 3x, 4x
perimeter = 2x + 3x + 4 x
144 = 2x + 3x + 4 x
x = 144 / 9
x = 16
now we substitude the value of x
2×16 = 32m = a
3×16= 48cm = b
4×16= 64 cm = c = base....
S = ( a+b+c)/2
(32 + 48 + 64 )/2
144/2 = 72
triangle area = √ s (s - a) (s-b) ( s-c)
triangle area
= √ 72 (72-32) (72-48) (72-64)
triangle area = √72 (40) (24) (8)
triangle area = √552960
triangle area=743.6128025cm²
Triangle area = ½ × base × height
743.6128025= ½ × 64 × height
743.6128025 = 32× height
height = 743.6128025/32
= 23.23790008 cm
The height corresponding to the longest side is 23.23790008cm.
i hope it helps you..
