Question

1. rectangle prst has diagonals $ps = 6x + 3$ and $rt = 7x - 2$. find the value of $x$.

a. 3
b. 4
c. 5
d. 6

Explanation:

Step1: Recall rectangle diagonal property

In a rectangle, the diagonals are equal in length. So, \( PS = RT \).

Step2: Set up the equation

Substitute the given expressions for \( PS \) and \( RT \): \( 6x + 3 = 7x - 2 \).

Step3: Solve for \( x \)

Subtract \( 6x \) from both sides: \( 3 = x - 2 \).
Add 2 to both sides: \( x = 3 + 2 = 5 \). Wait, no, wait, let's check again. Wait, \( 6x + 3 = 7x - 2 \), subtract \( 6x \): \( 3 = x - 2 \), then add 2: \( x = 5 \)? Wait, but let's check the options. Wait, maybe I made a mistake. Wait, \( 6x + 3 = 7x - 2 \), so \( 3 + 2 = 7x - 6x \), so \( 5 = x \)? But option C is 5. Wait, but let's verify. If \( x = 5 \), then \( PS = 6*5 + 3 = 33 \), \( RT = 7*5 - 2 = 33 \). Yes, that works. Wait, but the options have C as 5. Wait, but let's check the steps again.

Wait, the property of a rectangle: diagonals are congruent. So \( PS = RT \). So \( 6x + 3 = 7x - 2 \). Then, solving for \( x \):

\( 6x + 3 = 7x - 2 \)

Subtract \( 6x \) from both sides:

\( 3 = x - 2 \)

Add 2 to both sides:

\( x = 5 \)

So the answer is C. 5.

Answer:

C. 5