Review question

# What's the minimum area of this variable triangle? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R7212

## Suggestion

$OABC$ is a square of side $\quantity{1}{ft.}$. A point $X$ in $AB$ and a point $Y$ in $BC$ are such that $AX=\quantity{x}{ft.}$, $BY=\quantity{kx}{ft.}$ and $BY$ is longer than $AX$. For a given value of $k$, show that the minimum area of the triangle $OXY$ is $\quantity{\frac{4k-1}{8k}}{sq.ft.}$

Could we draw a picture of the problem?

Can we write the area of the triangle $OXY$ as a function of $x$?