Question

Given that the diagonals of a rectangle are congruent, express this relationship using the lengths of the diagonals EGEG and FHFH. If EG = 5x - 20EG=5x−20 and FH = 3x + 4FH=3x+4, determine the value of 'x' that makes the diagonals congruent. Solve for 'x'."

Answer 1

The diagonals of a rectangle are congruent when EG = 5x - 20 and FH = 3x + 4. To find the value of x, we set EG equal to FH and solve the equation.

Step-by-step explanation:

To express the relationship between the diagonals of a rectangle, we can start by stating that the diagonals are congruent, meaning they have the same length. Let's use the lengths of the diagonals EG and FH. Given that EG = 5x - 20 and FH = 3x + 4, we can set these two expressions equal to each other since the diagonals are congruent. So, 5x - 20 = 3x + 4. We can now solve this equation to find the value of x that makes the diagonals congruent.

Subtracting 3x from both sides, we get 2x - 20 = 4. Then, adding 20 to both sides, we have 2x = 24. Dividing both sides by 2, we find that x = 12. Therefore, when x = 12, the diagonals EG and FH are congruent.