given a right angles triangle ABC with right angle at B. Equilateral triangles PAB, QBC and RAC are describe on side AB, BC, CA respectively.
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given a right angles triangle ABC with right angle at B. Equilateral triangles PAB, QBC and RAC are describe on side AB, BC, CA respectively.
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Step-by-step explanation:
As all are equilateral ∆s,
=> A(PAB)=√3*(AB^2/4)
=> A(QBC)=√3*(BC^2/4)
=> A(RAC)=√3*(AC^2/4)
=> A(PAB+QBC)=√3/4*(AB^2+BC^2)
We know that AB^2 + BC^2 = AC^2 by Pythagorean theorem.
Substituting,
=> A(PAB+QBC)=√3/4 * AC^2
Further substituting,
=> A(PAB+QBC)=A(RAC)
Hence Proved.
Answer:
Step-by-step explanation: