Question

The sides of a triangle are in the ratio of 13:14:15 and its perimeter is 84 cm. Find the area of the triangle.​

Answer 1

$\huge\bold\red{HOLA!!}$

Here, perimeter of a triangle = 84 cm

Sides are in the ratio 13:14:15

Sum of ratio = 42 cm

13x84326 cm

4214x84%=28cm

4215C=.x8430cm

4284 :. S=. =42cm

By Heron's formula

Area = s(s - a)(s – b)(s

= 42(42–26)(42 – 28)(42– 30)

42 x 16 x 14 x 12 cm

= 2x3x 7 x 4x 4x2x7x3x 4 cm

= 2x3x7 x 4x2 cm

= 336 cm2

Hence, area of a triangle is 336cm^2

Answer 2

$\large{\underline{\underline{\mathfrak{\green{\sf{Solution:-}}}}}}$.

$\large{\underline{\underline{\mathfrak{\pink{\sf{Given\:Here:-}}}}}}$.

✴ Ratio of triangle sides = 13:14:15

✴ Perimeter of triangle = 84cm.

$\large{\underline{\underline{\mathfrak{\green{\sf{Find\:here:-}}}}}}$.

✴Sides of triangle .

✴Area of triangle .

$\large{\underline{\underline{\mathfrak{\pink{\sf{Explanation:-}}}}}}$.

➡let, Side of triangle will be

13x, 14x, 15x .

➡We, know that

✴Perimeter of triangle = Sum of all sides.

$\implies\:84\:=\:13x+14x+15x$.

$\implies\:42x\:=\:84$.

$\implies\:x\:=\frac{84}{42}$.

$\implies\:x\:=2$.

____________________

➡Side of triangle :-

✴First side = 13x = 13×2 = 26.cm

✴Second side = 14x =14×2= 28.cm

✴Third side = 15x =15×2=30cm

_______,,______________

➡Now , we Find Area .

Using Hero's Formula

where, p =half perimeter .

✴$\red{\:p\:= \frac{(sum\:of\:side )}{2}}$

$\implies\:p\:=\frac{26+28+30}{2}$.

$\implies\:p\:=\frac{84}{2}$.

$\implies\:p\:=\:42$.

➡So,

✴$\red{\:Area\:=\sqrt{p(p-a)(p-b)(p-c)}}$.

➡Here, a=26,b=28,c=30.

$\implies\:Area\:=\sqrt{42(42-26)(42-28)(42-30)}$.

$\implies\:Area\:=\sqrt{42*16*14*12}$.

$\implies\:Area\:=\sqrt{14*14*4*4*3*3*2*2}$.

$\implies\:Area\:=\:(\:14*4*3*2*)$.

$\implies\:Area\:=\:(336cm^2)$.

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