Question

Solve for x given that QRST is a rhombus.​

Answer 1

$\bold{\huge{\underline{ Solution }}}$

Given :-

• We have given Rhombus QRST
• The measurement of two sides of rhombus that is ( 6x - 5 ) and ( 4x + 13).

To Find :-

• We have to find the value of x

Let's Begin :-

Here, We have

• Rhombus QRST

We know that,

• All sides of rhombus are equal
• Opposite sides of rhombus are parallel to each other

Therefore,

From the figure, we can conclude that :-

$\bold{ 6x - 5 = 4x + 13 }$

$\sf{ 6x = 4x + 13 + 5 }$

$\sf{ 6x - 4x = 13 + 5 }$

$\sf{ 2x = 18 }$

$\sf{ x = }{\sf{\dfrac{18}{2}}}$

$\bold{ x = 9 }$

Hence, The value of x is 9 .

The measurement of the sides of rhombus QRST :-

Length of side QR

$\sf{ = 6x - 5 }$

$\sf{ = 6(9) - 5 }$

$\sf{ = 54 - 5 }$

$\bold{ = 49 }$

Length of side RS

$\sf{ = 4x + 13 }$

$\sf{ = 4(9) + 13 }$

$\sf{ = 36 + 13 }$

$\bold{ = 49 }$

From above we can say that,

• All sides of rhombus are equal.

Some more properties of rhombus

• Opposite angles of rhombus are equal
• Diagonals of rhombus bisect each other at 90°
• Diagonals of rhombus also bisect the side angles of rhombus
• Rhombus is a quadrilateral, so the sum of interior angles of rhombus are 360°
• Whereas, The sum of the adjacent angles of rhombus are 180°.
• All rhombus are parallelogram but all parallelograms are not rhombus .