Question

Refer to the pic given above and answer the question as fast as possible​

Answer 1

Solution

Given:-

• Perimeter of triangle = 8y²-9y+4
• first and second side are = 3y²-5y and 4y²+12

Find:-

• Third side of triangle

Explanation

Important Formula

★ Perimeter of triangle = Sum of all side of triangle

==> 8y²-9y+4 = (3y²-5y)+(4y²+12)+(Third side)

==> Third side = (8y²-9y+4)-(3y²-5y)+(4y²+12)

==> Third side = (8y²-9y+4)-(7y²-5y+12)

==> Third Side = 8y²-7y²+5y-9y+4-12

==> Third side = y²-4y-8 .

Hence

• Third side will be y²-4y-8

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Verification

Sum of all side will be perimeter of triangle .

So,

==> perimeter of triangle = Sum of all side

==> 8y²-9y+4 = (3y²-5y)+(4y²+12)+(y²-4y-8)

==> 8y²-9y+4 = (3y²+4y²+y²)+(-5y-4y)+(12-8)

==> 8y²-9y+4 = 8y²-9y+4

L.H.S. = R.H.S

That's proved.

Answer 2

Answer:

_________________________

$\bf \huge To \:Find \:$

• Third side of triangle

$\bf \huge Given \: \:$

• Perimeter of triangle = 8y²-9y+4
• Perimeter of triangle = 8y²-9y+4 first and second side are = 3y²-5y and 4y²+12

Accourding to the Formula

Perimeter of the triangle = sum of three sides

$\bf\: = 8y2 – 9y + 4\:$

Sum of two sides

$\bf \: = 3y^2 – 5y  + 4y^2 + 12</p><p>= 7y^2 − 5y + 12\:$

$\bf \: (8y2  – 9^y + 4)  – (7y^2  – 5y + 12)\:$

$\bf\:  = 8y^2  – 9^y + 4  – 7y^2 + 5y  – 12\:$

$\bf\: = y^2  – 4y  – 8\:$

Third side is $\bf</strong><strong>\: </strong><strong>= y^2  – 4y  – 8\:$