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

Question

area of a triangle is = 1/2*base*altitude

Answer 1

Let the sides be 13x, 14x, and 15x. Since the perimeter is 84, we have 13x+14x+15x=84, so that x=2, and the sides are therefore 26, 28, 30.

We now apply Heron's Formula for the area of a triangle in terms of its sides:

Let s be half the perimeter, and let a,b,c be the sides. Then the area is given by

sqrt{s(s-a)(S-b)(s-c)}.

Here, we have

s=42, a=26, b=28, c=30,

Area = 336.

Answer 2

You can use the hero's formula or try this
multiply by common multiple x, ratio becomes 13x:14x:15x
13x+14x:+15x=84 x=84/42=2
sides= 13*2, 14*2, 15*2= 26, 28, 30. Now draw the triangle with these sides. If u donot know what the base and altitude are sue the sine law to determine the angles. Then drop a perpendicular from any vertex. Figure out the length of altitude using trignometric ratio in the so formed right triangle. then find the area.

Answer 3

Solve for the semiperimeter first

13x + 14x + 15x = 84

42x = 84

x = 2

13 x 2 = 26
14 + 2 = 28
15 x 2 = 30

semiperimeter = a + b + c /2

26 + 28 + 30 = 84 / 2 = 42

Heron's formula

a = √s(s - a)(s - b)(s - c)

a = √42(42 - 26)(42 - 28)(42 - 30)

A = √42(16)(14)(12)

a = √112896

a = 336

The area of the triangle is 336 cm


- - - - - - s-

Answer 4

portion of Rt Triangle = a million/2 Base * properly Perimeter = A + B + C 36 = x + x + 3 + x + 6 upload Like words 36 = 3x + 9 element 36 = 3(x + 3) Divide both aspect by using 3 36/3 = 3(x+3) / 3 3's on the right aspect cancel to at least a million 12 = x + 3 Subtract 3 from both aspect 12-3 = x + 3 - 3 9 = x In a excellent Triangle the Hypotenuse (aspect opposite the RT perspective) is the longest aspect C is the Hypotenuse So section = a million/2 A*B section = a million/2 *(9) *(9+3) section = a million/2 *9*12 section = fifty 4

Answer 5

First, find the actual length of all the sides in cm. 13x + 14x + 15x = 84cm. Solve for x and then find the lengths

Then, use Hero's formula: first find s. s = .5 (a + b + c), where a, b, and c are the lengths of the triangle

to find the area: A = √(s (s-a) (s-b) (s-c))

Answer 6

[13+14+15]x=84
42x=84
x=2
13 x 2=26
14x 2 = 28
15 x 2= 30
area for scalene triangle is [s(s-a)(s-b)(s-c)]^1/2 where s= semiperimeter
semiperimeter=84/2=42
area=[42(42-26)(42-28)(42-30)]^1/2
=[42(16)(14)(12)]^1/2
=336[after simplifying]

Answer 7

13x + 14x + 15x= 84
42x = 84
so x = 2
13(2)+14(2)+15(2) = 26+28+30
the 3 sides are 26, 28, & 30

find out the area.


tan a = 26/30
a = 40.9°
sin 40.9 = h / 26
h = 17.1
17.1 * 30 / 2 = [255.4] <-- answer

Answer 8

let the sides be 13x, 14x, 15x
13x+14x+15x=84
42x=84
x=2
the sides are 26,28,30
these form pythagoream triplets, and so 30 is the hyp (the longest side)
so area = 1/2 * 28 * 26
= 14*26
= 364 sq. units

Answer 9

Think of it in terms of parts: 13x+14x+15x=84, so eventually u get each part to be 2, and then just find the area

Answer 10

given the ratio wehave 13x+14x+15x=84
42x=84
x=2
so sides are 26,28,30
we can find the area by the formula

area=s(sqrt((s-a)(s-b)(s-c))) where s=(a+b+c)/2
s=84/2=42
area=42(sqrt(16 x 14 x12))
=168sqrt(42) where sqrt(42)=6.48
=168 x 6.48
=1088.64