Squares in Triangles

Geometry Level 4

Let a triangle $ABC$ with $BC = 6 \text{ cm}$ , and the area of $30\text{ cm}^2$ . 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 $PQRS$ .

The answer is 3.75.

2 solutions

Alan Yan
Sep 12, 2015

$\frac{(6+x)x}{2} + \frac{x(10-x)}{2} = 30 \implies x = \frac{15}{4} = \boxed{3.75}$

Maria Kozlowska
Sep 12, 2015

Height of the triangle ABC can be computed as follows: $6*h/2=30 \Rightarrow h=10$ . $\triangle ABC \text{ is similar to } \triangle APQ \Rightarrow PQ/(10-PQ)= 6/10 \Rightarrow PQ=15/4=3.75$

Squares in Triangles

The answer is 3.75.

2 solutions

0 pending reports