the lengths of the sides of a triangl are in the ratio3:4:5,and its perimeter is 144cm. Find 1.the area of the triangle,and 2.the height corresponding to the longest side.
Answers
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 !
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..