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# Geometry

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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.

Dec 25, 2021

#1
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Find the side length s of the square PQRS.

Hello Guest!

$$A=30cm^2,\ a=6cm$$

$$A_{\triangle}=\frac{1}{2}ah=\frac{1}{2}\cdot 6cm\cdot h=30cm^2\\ \color{blue}h=10cm$$

$$h:(h-s)=a:s\\ hs=ah-as\\ s(a+h)=ah\\ s=\dfrac{ah}{a+h}=\dfrac{6cm\cdot 10cm}{6cm+10cm}$$

$$s=3.75cm$$

The side length of the square PQRS is s = 3.75cm.

!

Dec 25, 2021
#2
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Square side = x

BC = 6        AB = 10

10/6(6 - x) = 6/10(10 - x)

x = 3.75

Dec 26, 2021