Question

What is the value of x if the quadrilateral is a rhombus? please help

Answer 1

Answer:  The required value of x is 3.

Step-by-step explanation:  We are given to find the value of x if the quadrilateral shown in the figure is a rhombus.

From the figure, we note that

the lengths of the three sides of the rhombus are 5x units, (4x + 3) units and 15 units.

We know that the lengths of all the four sides of a rhombus are equal, so we get

$5x=4x+3=15\\\\\Rightarrow 5x=15\\\\\Rightarrow x=\dfrac{15}{5}\\\\\Rightarrow x=3.$

Thus, the required value of x is 3.

Answer 2

In a rhombus, all sides are equal:

5x = 15
and x = 15/5 = 3

(you could have done the same thing with the other side: 5x = 4x +3)