Question

If DF=7x-3 and EG=5x+9, find the value of X

Answer 1

• 6

`\:`

Explanation:

A rectangle is a parallelogram with equal angles and the diagonals of a rectangle are of equal length.

`\:`

Therefore,

`\\ { \longrightarrow \qquad{ \sf{ \pmb {DF = EG}}}} \: \: \\ \\`

`{ \longrightarrow \qquad{ \sf{ \pmb {7x - 3 = 5x + 9}}}} \: \: \\ \\`

Subtracting 5x from both sides we get :

`\\ { \longrightarrow \qquad{ \sf{ \pmb {7x - 5x - 3 = 5x - 5x + 9}}}} \: \: \\ \\`

`{ \longrightarrow \qquad{ \sf{ \pmb {2x - 3 = 9}}}} \: \: \\ \\`

Adding 3 to both sides we get :

`\\ { \longrightarrow \qquad{ \sf{ \pmb {2x - 3 + 3 = 9 + 3}}}} \: \: \\ \\`

`{ \longrightarrow \qquad{ \sf{ \pmb {2x = 12}}}} \: \: \\ \\`

Dividing 2 from both sides we get :

`\\ { \longrightarrow \qquad{ \sf{ \pmb { (2x)/(2) = (12)/(2) }}}} \: \: \\ \\`

`{ \longrightarrow \qquad{ \frak{ \pmb {x = 6}}}} \: \: \\ \\`

Therefore,

• The value of x is 6

Answer 2

`x=6`

Explanation:

Using the given measurements of the angles and the lengths of the sides, we can determine that this figure must be a rectangle.

Diagonals of a rectangle are always equivalent/congruent.

We can use this information to set up an equation:

`DF=EG\\7x-3=5x+9`

Add 3 to both sides:

`7x-3+3=5x+9+3\\7x=5x+12`

Subtract 5x from both sides:

`7x-5x=5x-5x+12\\2x=12`

Divide both sides by 2

`(2x)/(2)=(12)/(2)\\x=6`