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