Question

abcd is a rhombus. if bc = 5x − 7 and cd = 2x + 5, find the value of x and bc.

Explanation:

Step1: Recall rhombus side property

In a rhombus, all sides are equal. So \( BC = CD \).

Step2: Set up equation

Given \( BC = 5x - 7 \) and \( CD = 2x + 5 \), we set \( 5x - 7 = 2x + 5 \).

Step3: Solve for x

Subtract \( 2x \) from both sides: \( 5x - 2x - 7 = 5 \) → \( 3x - 7 = 5 \).
Add 7 to both sides: \( 3x = 5 + 7 \) → \( 3x = 12 \).
Divide by 3: \( x = \frac{12}{3} = 4 \).

Step4: Find BC

Substitute \( x = 4 \) into \( BC = 5x - 7 \): \( BC = 5(4) - 7 = 20 - 7 = 13 \).

Answer:

\( x = 4 \), \( BC = 13 \)