Question

Draw $X$ and $Y$ axes and mark the points $A(5,8)$ and $B(3,2)$.
(a) If we draw triangle $ABC$ such that the side $BC$ is parallel to the $X$ axis, what will be its height?
(b) Draw triangle $ABC$, such that the side $BC$ is parallel to the $X$ axis and area of the triangle is equal to $15$ square units.

Answer 1

(b) Consider the following figure.
The dotted line in blue represents the line $BC$, which is parallel to the x-axis.
So the height of the $△ABC$ is the perpendicular distance, marked by a dotted red line, from $A$ to the line $BC$.
Thus, the height of the $triangle=$ difference of y-coordinates of the point $A$ and the line $BC=82=6units$.
(c) Given that the area of the triangle is $15$ square units.
We know that area of triangle $=\frac{1}{2}\times base\times height$
Since $area=15$ square units, we have
$15=\frac{1}{2}\times base\times 6\Rightarrow \frac{15\times 2}{6}=base$
$\Rightarrow base=5units$
We can draw the triangle in two different ways, by marking $C$ to the left of $B$ and by marking $C$ to the right of $B$. Thus, the figure of the triangle can be as follows: