In the given figure, DE || BC and all measurements are given in centimetres. The length of AE is :

Step 1: Identify Similar Triangles

Given that DE is parallel to BC, we can conclude that triangle ADE is similar to triangle ABC. This is because corresponding angles are equal (angle D = angle B, angle E = angle C, and angle A is common).

Step 2: Set up Proportionality

For similar triangles, the ratio of their corresponding sides is equal. We can set up a proportion using the given side lengths.

Step 3: Substitute Known Values

We are given $AD = 2$ cm, $DB = 3$ cm, and $EC = 4.5$ cm. Therefore, $AB = AD + DB = 2 + 3 = 5$ cm, and $AC = AE + EC = AE + 4.5$ cm. Substitute these values into the proportionality equation.

Step 4: Solve for AE

Now, we solve the equation for AE. Cross-multiply and then isolate AE to find its value.

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