Use your result from part (a)(ii) to construct a line segment equal in length (in centimetres) to the square root of the length of the line segment $$ [T U] $$ which is drawn below.

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Allan Harmon · Accepted Answer

To construct a line segment equal in length to the square root of $$ [TU] $$, follow these steps: 1. **Draw $$ [TU] $$:** Mark points $$ T $$ and $$ U $$ on a straight line, with $$ TU $$ as the given length. 2. **Extend $$ [TU] $$ to $$ V $$:** Extend the line beyond $$ T $$ to point $$ V $$ such that $$ TV = TU $$. 3. **Find Midpoint $$ M $$:** Locate the midpoint $$ M $$ of $$ [TV] $$ using a compass. 4. **Draw Semicircle:** Draw a semicircle with diameter $$ [TV] $$ centered at $$ M $$. 5. **Erect Perpendicular at $$ U $$:** Draw a perpendicular line from $$ U $$ upwards, intersecting the semicircle at point $$ W $$. 6. **Resulting Segment $$ [UW] $$:** The length of $$ [UW] $$ is equal to $$ \sqrt{TU} $$. This geometric method uses similar triangles and the properties of semicircles to accurately determine the square root of the original line segment.

Use your result from part (a)(ii) to construct a line segment equal in length (in centimetres) to the square root of the length of the line segment \( [T U] \) which is drawn below.

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Use your result from part (a)(ii) to construct a line segment equal in length (in centimetres) to the square root of the length of the line segment \( [T U] \) which is drawn below.

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