Question

The perimeter of a
of a triangle is 40 cm.
one side is 7 m longer
than another side and 5 cm shorter than the thind side.
Find the
sides.​

Answer 1

Answer

Let us look what is perimeter .

Perimeter : Perimeter can be defined as the path or the boundary that surrounds a Shape.

Now, perimeter of triangle is : (length of ) side1 + side2 + side3.

⚝ Let side1 : a

⚝ Let side2 : b

⚝ Let side3 : c

According to the given conditions.

a + b + c = 40 cm ----------(1)

One side is 7cm longer than another side:

Let,

a = b + 7 ----------(2)

And is shorter than the third side by 5:

So,

a = c - 5

Or,

a - c = -5---------(3)

Let us add ' a + c ' on both side in equation (2)

We get,

⮕ a + a + c = b + 7 + a + c

⮕ 2a + c = a + b + c + 7

We know that a + b + c = 40(from equation (1))

So,

⮕ 2a + c = 40 + 7

2a + c = 47----------(4)

Add equations (3) and (4)

⮕ a - c + 2a + c = -5 + 47

⮕ 3a = 42

⮕ $\rm a = \frac { 42 } { 3 }$

$\implies \rm \boxed{a = 14 }$

Now putting this value in (2) we get,

$\implies \rm \boxed{b = 7 }$

Now putting a = 14 in (3) we get,

$\implies \rm \boxed{c = 19}$