Question

The perimeter of a triangle is 5x² - 2xy + 11y². If two sides are 3x² + zy and x² - 5xy - y² , find the third side​

Answer 1

Answer:

Third side = x² + 2xy + 12y²

Explanation:

Given,

Perimeter of a triangle is 5x² - 2xy + 11y²

Where two of them are 3x² + xy and x² - 5xy - y²

Find the third side.

We know that,

Perimeter of a triangle = a + b + c

Where, a, b, and c denotes the three sides of the triangle.

According to the question,

$\rm \implies \boldsymbol{ a + b + c} = {5x}^{2} - 2xy + 11 {y}^{2}$

$\rm \implies \: (3 {x}^{2} + xy) + ( {x}^{2} - 5xy - {y}^{2} ) + \boldsymbol c = {5x}^{2} - 2xy + 11 {y}^{2}$

$\rm \implies \: 3 {x}^{2} + xy+ {x}^{2} - 5xy - {y}^{2} + \boldsymbol c = {5x}^{2} - 2xy + 11 {y}^{2}$

$\rm \implies \: 4 {x}^{2} - 4xy - {y}^{2} + \boldsymbol c = {5x}^{2} - 2xy + 11 {y}^{2}$

$\rm \implies \: - 4xy - {y}^{2} + \boldsymbol c = {5x}^{2} - 2xy + 11 {y}^{2} - 4 {x}^{2}$

$\rm \implies \: - 4xy - {y}^{2} + \boldsymbol c = {x}^{2} - 2xy + 11 {y}^{2}$

$\rm \implies \: - {y}^{2} + \boldsymbol c = {x}^{2} - 2xy + 11 {y}^{2} + 4xy$

$\rm \implies \: - {y}^{2} + \boldsymbol c = {x}^{2} + 2xy + 11 {y}^{2}$

$\rm \implies \: \boldsymbol c = {x}^{2} + 2xy + 11 {y}^{2} + {y}^{2}$

$\rm \implies \: \boldsymbol c = {x}^{2} + 2xy + 12 {y}^{2}$

∴ The third side of the triangle is x² + 2xy + 12y²

Answer 2

Answer:

Perimeter of a rectangle is 2(L+B)

Given, two adjacent sides are 5x

2

+2xy−13,2x

2

−6xy+11

Therefore,

2(L+B)

=2(5x

2

+2xy−13+2x

2

−6xy+11)

=2(7x

2

−4xy−2)

=14x

2

−8xy−4