Let a triangle ABC with BC = 6 cm, and the area of 30 cm2. A square PQRS is inscribed so that points S and R is on BC, Q on AC, and P on AB respectively. Find the side length of the square PQRS.
+14913 Find the side length s of the square PQRS.
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\(A=30cm^2,\ a=6cm\)
\(A_{\triangle}=\frac{1}{2}ah=\frac{1}{2}\cdot 6cm\cdot h=30cm^2\\ \color{blue}h=10cm\)
\(h:(h-s)=a:s\\ hs=ah-as\\ s(a+h)=ah\\ s=\dfrac{ah}{a+h}=\dfrac{6cm\cdot 10cm}{6cm+10cm}\)
\(s=3.75cm\)
The side length of the square PQRS is s = 3.75cm.
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