Question

question 1.6
in trapezoid (abcd), (dc = 289), (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

We know $MN=167$, $DC=199$, and $AB=3x+7$. Plug these into the formula:
$$167 = \frac{(3x + 7) + 199}{2}$$

Step3: Multiply both sides by 2

Eliminate the denominator by multiplying each side by 2:
$$167 \times 2 = 3x + 7 + 199$$
$$334 = 3x + 206$$

Step4: Isolate the variable term

Subtract 206 from both sides to isolate the term with $x$:
$$334 - 206 = 3x$$
$$128 = 3x$$

Step5: Solve for x

Divide both sides by 3 to solve for $x$:
$$x = \frac{128}{3} \approx 42.67$$

Answer:

$x = \frac{128}{3}$ (or approximately 42.67)