#### Question

Draw a line segment AB of length 7 cm. Using ruler and compasses, find a point P on AB such that `(AP)/(AB)=3/5`.

#### Solution

It is given that`(AP)/(AB)=3/5`.

`therefore (AP)/(PB)=(AP)/(AB-AP)=3/(5-3)=3/2`

Thus, point P divides line segment AB in the ratio 3: 2.

To draw a line segment AB of length 7 cm and mark a point P (using ruler and compass) such that `(AP)/(PB)=3/5 i,e, (AP)/(PB)=3/2`, the following steps are to be followed:

**Step 1:** Draw line segment AB of length 7 cm and draw a ray AX making an acute angle with line segment AB.

**Step 2:** Locate 5 (2 + 3) points i.e., A_{1}, A_{2}, A_{3}, A_{4} and A_{5} on AX such that AA_{1} = A_{1} A_{2} = A_{2} A_{3} and so on.

**Step 3:** Join BA_{5}.

**Step 4:** Through point A_{3} , draw a line parallel to BA_{5} (by making an angle equal to ∠AA_{5} B) at A_{3} intersecting AB at point P.

Now, P is the required point on line segment AB of length 7 cm. This point satisfies the condition`(AP)/(AB)=3/5`.