Question

The sum of three sides of a triangle is 16 3/5 CM. If two of it's measure 5 7/10cm and 6 3/4cm respectively, then the length of the third side is

Answer 1

Question

The sum of three sides of a triangle is 163/5 CM. If two of it's measure 57/10cm and 63/4cm respectively, then the length of the third side is ?

Solution

Given:-

• The sum of three sides of a triangle is 163/5 CM.
• Two side are 57/10 cm & 63/4 cm.

Find:-

• Length of third sides

Explanation

We know,

Sum of all side of triangle be perimeter of triangle .

So,

we can say that 163/5 cm be perimeter of triangle ∆ABC

Let,

• AB = 57/10 cm
• BC = 63/4 cm

CA be the Third side of ∆ABC

★ perimeter of triangle = Sum of all side of triangle

==> 163/5 = AB + BC + CA

==> 163/5 = 57/10 + 63/4 + CA

==> CA = 163/5 - [ 57/10 + 63/4 ]

==> CA = 163/5 - [ (114+315)/20 ]

==> CA = 163/5 - [ 429/20 ]

==> CA = 163/5 - 429/20

==> CA = (652 - 429 )/20

==> CA = 223/20

Hence

• Third side will be of ∆ABC = 223/20 cm.

__________________

Verification

We prove here, Sum of all sides ∆ABC will be = 163/5 cm

So,

==> 163/5 = 57/10 + 63/4 + 223/20

==> 163/5 = (114 + 315 + 223)/20

==> 163/5 = 652/20

==> 163/5 = 163/5

LH.S. = R.H.S.

That's proved.

Here, Sum of all side = 163/5 cm

__________________

Answer 2

✬ Length of third side = 10.9 cm

Step-by-step explanation:

Given:

• Sum of all three sides of triangle is 163/5 cm.
• Measure of first side is 57/10 cm.
• Measure of second side is 64/4 cm.

To Find:

• What is the length of third side of the triangle ?

Solution: Let ABC be a triangle where

• AB = 57/10 cm = 5.7 cm
• BC = 64/4 cm = 16 cm
• CA = ?

★ Perimeter of triangle = Sum of its all sides ★

But perimeter given is 163/5 cm = 32.6 cm

A/q

$\implies{\rm }$ (AB + BC + CA) cm = 32.6 cm

$\implies{\rm }$ (5.7 + 16 + CA) cm = 32.6 cm

$\implies{\rm }$ (21.7 + CA) cm = 32.6 cm

$\implies{\rm }$ CA = (32.6 – 21.7) cm

$\implies{\rm }$ CA = 10.9 cm

Hence, the length of third side of third side CA of triangle ABC is of 10.9 cm or 109/10 cm

____________

★ ChEck ★

➽ AB + BC + CA = 32.6

➽ 5.7 + 16 + 10.9 = 32.6

➽ 32.6 cm = 32.6 cm { LHS = RHS }

Since, 32.6 cm = 326/10 = 163/5 cm