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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.

Apr 6, 2022

#1
+13896
+3

Find the side length of the square PQRS.

Hello Guest!

The height of the triangle is h.

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

$$Prerequisite\ for\ a\ square\ on\ \overline{BC}.\\ 90^o\geq \ ∠ABC\ \geq arctan(\frac{10}{6})\\$$

The side length of the square is x.

$$(10-x):10=x:6\\ 60-6x=10x\ |\ +6x\\ 60=16x\ |\ :16\\ \frac{60}{16}=x\\ \color{blue}x=3.75$$

The side length of the square PQRS is 3.75cm.

!

Apr 6, 2022
edited by asinus  Apr 6, 2022
edited by asinus  Apr 6, 2022
edited by asinus  Apr 6, 2022
edited by asinus  Apr 6, 2022

#1
+13896
+3

Find the side length of the square PQRS.

Hello Guest!

The height of the triangle is h.

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

$$Prerequisite\ for\ a\ square\ on\ \overline{BC}.\\ 90^o\geq \ ∠ABC\ \geq arctan(\frac{10}{6})\\$$

The side length of the square is x.

$$(10-x):10=x:6\\ 60-6x=10x\ |\ +6x\\ 60=16x\ |\ :16\\ \frac{60}{16}=x\\ \color{blue}x=3.75$$

The side length of the square PQRS is 3.75cm.

!

asinus Apr 6, 2022
edited by asinus  Apr 6, 2022
edited by asinus  Apr 6, 2022
edited by asinus  Apr 6, 2022
edited by asinus  Apr 6, 2022