find the value of x in this trapezoid.

$x = ? $

Question

find the value of x in this trapezoid.

$x =  ? $

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Linear Equations" ], "new_concepts": [ "Trapezoid Midsegment Theorem" ], "current_concepts": [ "Trapezoid Midsegment Theorem", "Linear Equations" ] } ## Identify the midsegment of the trapezoid The tick marks on the non-parallel sides (legs) of the trapezoid indicate that the segment with length $20$ connects the midpoints of the legs. Therefore, this segment is the midsegment of the trapezoid. ## Set up the midsegment equation The length of the midsegment of a trapezoid is the average of the lengths of the two parallel bases: $$ 20 = \frac{(2x + 6) + (4x + 4)}{2} $$ ## Solve for x $$ \begin{aligned} 20 &= \frac{6x + 10}{2} \ 20 &= 3x + 5 \ 15 &= 3x \ x &= 5 \end{aligned} $$ Find the value of x in this trapezoid. $x =$ 5 { "elements": [ { "type": "point", "params": [[-3, 2]], "properties": { "name": "A", "visible": false } }, { "type": "point", "params": [[3, 2]], "properties": { "name": "B", "visible": false } }, { "type": "point", "params": [[5, -2]], "properties": { "name": "C", "visible": false } }, { "type": "point", "params": [[-5, -2]], "properties": { "name": "D", "visible": false } }, { "type": "segment", "params": [[-3, 2], [3, 2]], "properties": { "strokeColor": "#583C87", "strokeWidth": 3 } }, { "type": "segment", "params": [[3, 2], [5, -2]], "properties": { "strokeColor": "#583C87", "strokeWidth": 3 } }, { "type": "segment", "params": [[5, -2], [-5, -2]], "properties": { "strokeColor": "#583C87", "strokeWidth": 3 } }, { "type": "segment", "params": [[-5, -2], [-3, 2]], "properties": { "strokeColor": "#583C87", "strokeWidth": 3 } }, { "type": "point", "params": [[-4, 0]], "properties": { "name": "M", "visible": true, "color": "#8C55F2" } }, { "type": "point", "params": [[4, 0]], "properties": { "name": "N", "visible": true, "color": "#8C55F2" } }, { "type": "segment", "params": [[-4, 0], [4, 0]], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 3 } }, { "type": "text", "params": [0, 2.4, "2x + 6"], "properties": { "color": "#583C87" } }, { "type": "text", "params": [0, 0.4, "20"], "properties": { "color": "#8C55F2" } }, { "type": "text", "params": [0, -2.6, "4x + 4"], "properties": { "color": "#583C87" } } ] } { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Trapezoid Midsegment Theorem" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the midsegment of the trapezoid

Set up the midsegment equation

Solve for x

Answer: