Question

the difference of semi perimeter and sides of a triangle ABC are 8cm,7cm and 5cm respectively.find the area and the semiperimeter

Answer 1

Consider a, b and c as the sides of a triangle and s as the semi perimeter

So we get

s - a = 8cm

s - b = 7cm

s - c = 5cm

We know that(s - a) + (s - b) + (s - c) = 8 + 7 + 5

On further calculation

3s - (a + b + c) = 20

We know that a + b + c = 2s

3s - 2s = 20

So we gets = 20

By substituting the value of s

a = s - 8 = 20 - 8 = 12cm

b = s - 7 = 20 - 7 = 13cm

c = s - 5 = 20 - 5 = 15cm

We know that

Area=

s(s−a)(s−b)(s−c)

By substituting the values

Area=

20(20−12(20−13)(20−15)

So we get

Area=

20×8×7×5

It can be written as

Area=

4×5×4×2×7×5

By multiplication

Area=20

14

answer - 20 √14 cm^2