Question

find the area of triangle two sides 16 and 22cm and perimeter is 64cm​

Answer 1

Answer:

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2

Step-by-step explanation:

hope it will helpful to you

Answer 2

Given :-

First side = 16 cm

Second side = 22 cm

Perimeter = 64 cm

To Find :-

The area of triangle.

Analysis :-

Firstly, find the third side of the triangle by adding the two sides and subtracting their sum from the perimeter.

Then find the semi perimeter by dividing the perimeter given by 2.

Finally, using Heron's formula find the area.

Solution :-

We know that,

• p = Perimeter
• a = Area
• s = Semi perimeter

Let the third side be 'x'.

Given that,

First side = 16 cm

Second side = 22 cm

Perimeter = 64 cm

Making an equation,

x + 16 + 22 = 64

x + 38 = 64

By transposing,

x = 64 - 38

x = 26 cm

Therefore, the third side is 26 cm.

Finding semi perimeter,

$\underline{\boxed{\sf Semi \ perimeter= \dfrac{a+b+c}{2} }}$

Given that,

Perimeter (p) = 64 cm

First side (a) = 16 cm

Second side (b) = 22 cm

Third side (c) = 26 cm

Substituting their values,

16+22+26/2 = 64/2

= 32 cm

Therefore, the semi perimeter is 32 cm.

Using Heron's formula,

$\underline{\boxed{\sf Area \ of \ triangle= \sqrt{s(s-a)(s-b)(s-c)} }}$

Given that,

Semi perimeter (p) = 32 cm

First side (a) = 16 cm

Second side (b) = 22 cm

Third side (c) = 26 cm

Substituting their values,

$\sf =\sqrt{32(32-16)(32-22)(32-26)}$

$\sf =\sqrt{32 \times 16 \times 10 \times 6}$

$\sf =\sqrt{ 30720}$

$\sf =32\sqrt{30} \ cm^2$

Therefore, area of the triangle is 32√30 cm².