The sides of triangles PQR and ABC are given; PQ = 16cm, QR = 20cm, PR = 28cm and AB = 12cm,

The sides of triangles PQR and ABC are given; PQ = 16cm, QR = 20cm, PR = 28cm and AB = 12cm, BC = 15cm, AC = 21cm. Find the ratio of the areas of these triangles

To solve the problem, we use Heron’s formula, which allows us to find the area of any triangle along its sides:

S = √p (p – a) (p – b) (p – c);

Here p is half of the perimeter p = (a + b + c) / 2;

Let’s calculate what these values are for each of the triangles:

Triangle ABC

R

(12 + 15 + 21) / 2 =

48

p – a

48 – 12 =

36

p – b

48 – 15 =

33

p – with

48 – 21 =

27

p (p – a) (p – b) (p – c)

48 × 36 × 33 × 27 =

1,539,648

S

√ 1 539 648

1240,7852

PQR triangle

R

(16 + 20 + 28) / 2 =

32

p – a

32 – 16 =

sixteen

p – b

32 – 20 =

12

p – with

32 – 28 =

4

p (p – a) (p – b) (p – c)

32 × 16 × 12 × 4 =

24,576

S

√ 24,576

156.7673

Find the area ratio:

SABC / S PQR = 1241: 157 = 7.9;