Leaning Over
Weekly Problem 31 - 2017
The triangle HIJ has the same area as the square FGHI. What is the distance from J to the line extended through F and G?
The triangle HIJ has the same area as the square FGHI. What is the distance from J to the line extended through F and G?
Age
11 to 14
Challenge level
Problem
Image
The triangle $HIJ$ has the same area as the square $FGHI$.
$FG$ has a length of 4cm.
What is the perpendicular distance from $J$ to the extension of the line $FG$?
If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.
Student Solutions
The triangle $HIJ$ has a base ($HI$) of $4\text{cm}$, the same as the side of the square.
The area of the square is $4 \times 4 = 16\text{cm}^2$, so this is also the area of the triangle.
If the perpendicular height of $HIJ$ is $h$, then $\frac{1}{2}\times 4\times h = 16$. This means $2h = 16$, so $h=8\text{cm}$.
$J$ is therefore $8\text{cm}$ above the top of the square, which is $4\text{cm}$ above the base, making a total of $12\text{cm}$.