Question

“who wants to be a millionaire? (properties of rectangles pyramid)
directions: solve each problem to find the value of x given that the quadrilateral is a rectangle. find its matching answer in the answer box and decode the answer to the riddle using the letter of the answer associated with each question. show all of your work.
answer
b 6 x 7 12 14 u 1 10 7 i 2 9 7 4
14 11 x 8 7 14 d 3 y 4 7 15 u 5 9 2 13

1. x = 10

7x = 12
diagram of a rectangle with 4x + 18 and a right angle

1. x = 6

(13x + 12)°
diagram of a rectangle with a right angle

1. x = 19

diagram of a rectangle with diagonals, 4x + 88 and 8x - 18

1. x = 13

diagram of a rectangle with diagonals, 14x - 9 and 16x - 35

1. x = 7

diagram of a rectangle with 3x + 6 and 10x - 43, right angle

1. x = 17

diagram of a rectangle with (5x + 16)° and (3x - 62)°, right angle”

Explanation:

Step1: Set sides equal (rectangle)

$4x + 18 = 7x - 12$

Step2: Rearrange to solve for x

$18 + 12 = 7x - 4x$
$30 = 3x$
$x = \frac{30}{3} = 10$

Step3: Use right angle property

$13x + 12 = 90$

Step4: Solve for x

$13x = 90 - 12$
$13x = 78$
$x = \frac{78}{13} = 6$

Step5: Set diagonals equal (rectangle)

$4x + 28 = 8x - 12$

Step6: Rearrange to solve for x

$28 + 12 = 8x - 4x$
$40 = 4x$
$x = \frac{40}{4} = 10$

Step7: Set diagonals equal (rectangle)

$14x - 9 = 16x - 35$

Step8: Rearrange to solve for x

$35 - 9 = 16x - 14x$
$26 = 2x$
$x = \frac{26}{2} = 13$

Step9: Set sides equal (rectangle)

$3x + 6 = 10x - 43$

Step10: Rearrange to solve for x

$6 + 43 = 10x - 3x$
$49 = 7x$
$x = \frac{49}{7} = 7$

Step11: Use angle property (rectangle)

$5x + 16 + 3x - 62 = 90$

Step12: Simplify and solve for x

$8x - 46 = 90$
$8x = 90 + 46$
$8x = 136$
$x = \frac{136}{8} = 17$

Answer:

1. $x = 10$
2. $x = 6$
3. $x = 10$
4. $x = 13$
5. $x = 7$
6. $x = 17$