As shown in the figure, a square is drawn sharing one corner with a right triangle and the other three corners on the sides of this triangle. Calculate the length of a side of the square.
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Solution
Let's name the corners as shown below.
Given : AD = 4 cm
FC = 3 cm
DEFB is a square
Let the length of each side of thesquare be x.
⇒DE=EF=FB=DB=x
Each interior angle of the square will be equal to 90∘.
Since BDEF is a square, DE||BF||BC and ∠ADE=∠ABC (Corresponding angles are equal)
In △ADE and △ABC,∠ADE=∠ABC∠AED=∠ACB (Corresponding angles are equal)