Question

Given $AB$ of length $7.3cm$ and $CD$ of length $3.4cm$. Construct a line segment $XY$ such that the length of $XY$ is equal to the difference between the lengths of $AB$ and $CD$ verify by measurement.

Answer 1

Step $1:$ Draw two line segments $AB$ and $CD$ of given length.

Draw a line segment $AB$ of length $7.3cm$ with the help of ruler.

Draw a line segment $CD$ of length $3.4cm$ with the help of ruler.

Step $2:$ Draw the line segment $XY$.

Adjust the compass to the length of segment $CD$ and draw an arc on the line segment $AB$ from the point $A$ and mark the point as $P$.

Draw a line $l$ and mark one end as $X$.

Adjust the compass to the length of segment $PB$ and draw an arc on line $l$ from the point $X$ towards another end and mark the point as $Y$.

Step $3$:Compute the difference between the lengths of $AB$ and $CD$.

$7.3-3.4=3.9cm$

Use the ruler to measure the length of line $XY$, which comes out $3.9cm$.

Hence, the length of $XY$ is equal to the difference between the lengths of $AB$ and $CD$.