The length of the sides of a triangle are in the ratio 5:43 and its semi perimeter is 72cm . find the area of the triangle and the height correspnding to the longer side .
Answers
It will be 5:4:3 not 5:43
Let the sides in the ratios be x
So the sides will be 5x and 4x and 3x
Semi perimeter=72
Perimeter=72 multiplied by 2= 144
ATQ
5x+4x+3x=144{Perimeter of a triangle= sum of all sides}
12x=144
x=144/12
x=12
sides will be
5x=5 multiplied by 12=60
4x=4 multiplied by 12=48
3x=3 multiplied by 12=36
Hence find the area by heron's formula that is
√s(s-a)(s-b)(s-c)
And when the area will come
by const draw an height corresponding to the longer side
and then use this formula:-
area of triangle=1/2bh
we have area of triangle that had came by using heron's formula and we have also base
put the values
your answer will come
Step-by-step explanation:
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.
3x+4x+5x=1443x+4x+5x=144
12x=14412x=144
x=12x=12
The value of x is 12. It means the length of sides are 36,48,60.
Using heron's formula the area of triangle is
A=\sqrt{s(s-a)(s-b)(s-c)}A=
s(s−a)(s−b)(s−c)
Where,
s=\frac{a+b+c}{2}s=
2
a+b+c
s=\frac{144}{2}=72s=
2
144
=72
The area of triangle is
A=\sqrt{72(72-36)(72-48)(72-60)}=864A=
72(72−36)(72−48)(72−60)
=864
The area of triangle is 864 cm².
The area of triangle is
A=\frac{1}{2}\times base \times heightA=
2
1
×base×height
864=\frac{1}{2}\times 60 \times height864=
2
1
×60×height
height=\frac{864}{30}=28.8height=
30
864
=28.8
The height corresponding to the longest side is 28.8 cm.