Question

question 1-5
in trapezoid cdab, dc = 229, mn = 187 and ab = 3x + 7. find x.

Explanation:

Step1: Recall trapezoid midsegment formula

The midsegment (or median) of a trapezoid is equal to the average of the lengths of the two parallel sides. The formula is:
$$MN = \frac{AB + DC}{2}$$

Step2: Substitute given values

Plug in $MN=187$, $DC=229$, and $AB=3x+7$ into the formula:
$$187 = \frac{(3x + 7) + 229}{2}$$

Step3: Multiply both sides by 2

Eliminate the denominator by multiplying each side by 2:
$$187 \times 2 = 3x + 7 + 229$$
$$374 = 3x + 236$$

Step4: Isolate the term with x

Subtract 236 from both sides:
$$374 - 236 = 3x$$
$$138 = 3x$$

Step5: Solve for x

Divide both sides by 3:
$$x = \frac{138}{3}$$

Answer:

$x = 46$