Answer:
The value of x is 3.
Step-by-step explanation:
Consider the below figure attached with this question.
Given: Quadrilateral QUAD is a rectangle, DU=26 and QP=2x+7.
We need to find the value of x.
Diagonals of a rectangle are equal.
[tex]QA=DU=26[/tex] .... (1)
Diagonals bisect each other.
[tex]QP=UP=AP=DP=2x+7[/tex] .... (2)
Using (1) and (2) we get
[tex]DU=QP+AP[/tex]
[tex]DU=QP+QP[/tex]
[tex]DU=2QP[/tex]
Substitute given values.
[tex]26=2(2x+7)[/tex]
[tex]26=4x+14[/tex]
[tex]26-14=4x[/tex]
[tex]12=4x[/tex]
Divide both sides by 3.
[tex]3=x[/tex]
Hence, the value of x is 3.
