Question

. The perimeter of a triangle is (7x - 3y + 6) metre. The lengths of two sides of the triangle are (2x + y - 1) metre and (x - 2y + 10) metre. Find the length of the third side in terms of x and y.​

Answer 1

Answer:

4x - 2y - 3

Step-by-step explanation:

Sum of other 2 sides are (2x+y-1) + (x-2y+10)

= 3x - y + 9

Third side = Perimeter - Sum of other sides

= (7x-3y+6) - (3x-y+9)

= 7x-3y+6 - 3x+y-9

= 4x - 2y - 3

Answer 2

SOLUTION

GIVEN

• The perimeter of a triangle is (7x - 3y + 6) metre.

• The lengths of two sides of the triangle are (2x + y - 1) metre and (x - 2y + 10) metre.

TO DETERMINE

The length of the third side in terms of x and y.

EVALUATION

Here it is given that the perimeter of a triangle is (7x - 3y + 6) metre.

The lengths of two sides of the triangle are (2x + y - 1) metre and (x - 2y + 10) metre.

Let length of the third side = z

Perimeter = (7x - 3y + 6)

So we have

Sum of the three sides = (7x - 3y + 6)

$\displaystyle \sf{ \implies (2x + y - 1) + (x - 2y + 10) + z = (7x - 3y + 6)}$

$\displaystyle \sf{ \implies (3x - y + 9)+ z = (7x - 3y + 6)}$

$\displaystyle \sf{ \implies z = (7x - 3y + 6) -(3x - y + 9) }$

$\displaystyle \sf{ \implies z = 7x - 3y + 6 - 3x + y - 9}$

$\displaystyle \sf{ \implies z = 4x - 2y - 3}$

FINAL ANSWER

Hence length of the third side

= 4x - 2y - 3 metre

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