A right triangle inside a square

Geometry Level 3

Triangle $AEF$ is a right triangle with $AE=4$ and $EF=3$ . The triangle is inscribed inside a square $ABCD$ such that $E$ lies on $BC$ and $F$ lies on $CD$ .

What is the area of the square $ABCD$ to 3 decimal places?

Note: The triangle is right-angled at $E$ .

The answer is 15.058.

1 solution

Marta Reece
Feb 27, 2017

$x^2+y^2=16$

$x^2+z^2=25$

$(x-y)^2+(x-z)^2=9$

Substituting from the first two equations into the last we can get

$x(y+z)=16$

Substituting a second time, we get an equation in $x$ :

$x(\sqrt{16-x^2}+\sqrt{25-x^2})=16$

The applicable solution is $x=3.88057$ , the other $(x=1.9846)$ being far too small, so the answer is then $x^2=15.0588\approx15.059$ .

A right triangle inside a square

The answer is 15.058.

1 solution

0 pending reports