Question

Quadrilateral CAMP below is a rhombus. the length PQ is (x+2) units, and the length of QA is (3x-14) units. Which statements best explains why the equation x+2 = 3x-14 can be use to find x?

Answer 1

Answer:

Q cuts the diagonal PA into 2 equal halves, since the diagonals of rhombus meet at right angles.

The value of x is 8.

Step-by-step explanation:

Given that Quadrilateral CAMP below is a rhombus. the length PQ is (x+2) units, and the length of QA is (3x-14) units

From the given Q is the middle point, which cut the diagonal PA into 2 equal halves.

By the definition of rhombus, diagonals meet at right angles.

Implies that PQ = QA

x+2 = 3x - 14

x-3x=-14-2

-2x=-16

2x = 16

dividing by 2 on both sides, we will get,

$x =\frac{16}{2}$

∴ x=8

Since Q cuts the diagonal PA into 2 equal halves, since the diagonals of rhombus meet at right angles we can equate x+2 = 3x-14 to find the value of x.

The line segment $\overrightarrow{PA}=\overrightarrow{PQ}+\overrightarrow{QA}$

$\overrightarrow{PA}=x+2+3x-14$

$=4x-12$

$=4(8)-12$ ( since x=8)

$=32-12$

$=20$

∴ $\overrightarrow{PA}=20$ units