Question

c) The perimeter of triangle 8+13a + 7a² and Two
of its sides are 2a²+ 3a+2 and 3a²-4a-1 find the
third side of triangle
​

Answer 1

Answer:

Step-by-step explanation:

Let X , Y, Z are three sides of triangle & P be the perimeter of triangle

where X=2a^2+3a+2

Y=3a^2-4a-1 Z=?

P=7a^2+13a+8

Now

P= X+Y+Z

7a^2+13a+8=2a^2+3a+2+3a^2-4a-1 +Z

7a^2+13a+8=5a^2-a+1+1

Z=7a^2-5a^2+13a+a+8-1

Z=2a^2+14a+7

Hence , the third side of triangle =2a^2+14a+7.

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Answer 2

• The third side of the triangle = 7 + 14a + 2a².

Given :–

• Perimeter of the triangle = 8 + 13a + 7a².
• The first side of the triangle = 2a² + 3a + 2.
• The second side of the triangle = 3a² – 4a – 1.

To Find :–

• The third side of the triangle.

Solution :–

Let,

The third side of the triangle be x.

Given that,

Perimeter of the triangle = 8 + 13a + 7a²

That means,

First side + Second side + Third side = 8 + 13a + 7a²

We have,

• First side = 2a² + 3a + 2.
• Second side = 3a² – 4a –1.

Now, substitute this value.

$\rightarrow ( {2a}^{2} + 3a + 2) + ( {3a}^{2} - 4a - 1) + x = 8 + 13a + {7a}^{2}$

$\rightarrow {2a}^{2} + 3a + 2 + {3a}^{2} - 4 - 1 + x = 8 + 13a + {7a}^{2}$

$\rightarrow {2a}^{2} + {3a}^{2} + 3a - 4a + 2 - 1 + x = 8 + 13a + {7a}^{2}$

$\rightarrow {5a}^{2} - a + 1 + x = 8 + 13a + {7a}^{2}$

$\rightarrow x = (8 + 13a + {7a}^{2} ) - ( {5a}^{2} - a + 1)$

$\rightarrow x = 8 + 13a + {7a}^{2} - {5a}^{2} + a - 1$

$\rightarrow x = 8 - 1 + 13a + a + {7a}^{2} - {5a}^{2}$

$\rightarrow x = 7 + 14a + {2a}^{2}$

Hence,

The third side of the triangle is 7 + 14a + 2a².

Verification :–

First side + Second side + Third side = 8 + 13a + 7a²

Now we have,

• First side = 2a² + 3a + 2.
• Second side = 3a² – 4a –1.
• Third side = 7 + 14a + 2a².

Now, substitute all the values.

$\rightarrow ( {2a}^{2} + 3a + 2) + ( {3a}^{2} - 4a - 1) + (7 + 14a + {2a}^{2} ) = 8 + 13a + {7a}^{2}$

$\rightarrow {2a}^{2} + 3a + 2 + {3a}^{2} - 4a - 1 + 7 + 14a + {2a}^{2} = 8 + 13a + {7a}^{2}$

$\rightarrow 2 - 1 + 7 + 3a - 4a + 14a + {2a}^{2} + {3a}^{2} + {2a}^{2} = 8 + 13a + {7a}^{2}$

$\rightarrow 1 + 7 - a + 14a + {5a}^{2} + {2a}^{2} = 8 + 13a + {7a}^{2}$

$\rightarrow 8 + 13a + {7a}^{2} = 8 + 13a + {7a}^{2}$

Hence Verified !!