Question

Base of a triangle is 9 and the height is 5. Base of another triangle is 10 and height is 6. Find the ratio of areas of these triangles.

Answer 1

Hint: . Until and unless it is not pointed out in the question that the triangle we are talking about is a equilateral triangle we should always use the formulae of area for the right angled triangle i.e.
Area of triangle = $\dfrac{1}{2} \times Base \times Height$
2. To find the ratio of two areas we are always going to use the formulae
Ratio = $\dfrac{{{A_1}}}{{{A_2}}}$
Where $A_1$ stands for Area of triangle 1
And $A_2$ stands for Area of triangle 2

Complete step by step answer:
 1. Let’s assume the area of first triangle = $A_1$
And, the area of the second triangle = $A_2$.
2. In the triangle we are provided with the data that the height of the triangle is 9 units and the base is 5 units.
3. Therefore, By using the area of triangle
= $\dfrac{1}{2} \times Base \times Height$
4. By substituting the dimensions of first triangle in the formulae we will get the area of first triangle
$\begin{gathered}
  {A_1} = \dfrac{1}{2} \times 9 \times 5 \\
  {A_1} = \dfrac{{45}}{2} \\
\end{gathered} $
Therefore, the area of the first triangle is $\dfrac{{45}}{2}$ $unit^2$.
5. Now, by substituting the dimensions of second triangle in the same formulae we will get the area of second triangle
$\begin{gathered}
  {A_2} = \dfrac{1}{2} \times 10 \times 6 \\
  {A_2} = \dfrac{{60}}{2} \\
\end{gathered} $
Therefore the area of the second triangle is $\dfrac{{60}}{2}$ $unit^2$.
6. Now, for finding the ratio of the area of first triangle and the second triangle we will be using the formulae
Ratio = $\dfrac{{{A_1}}}{{{A_2}}}$
Where $A_1$ is the area of the first triangle and $A_2$ is the area of the second triangle.
Therefore, substituting the values of $A_1$ and $A_2$ in the we will get
$\begin{gathered}
   = \dfrac{{\dfrac{{45}}{2}}}{{\dfrac{{60}}{2}}} \\
   = \dfrac{{45}}{{60}} \\
\end{gathered} $
Diving by 15 in numerator and denominator, we will get
$ = \dfrac{3}{4}$
Therefore, the ratio of areas of first triangle and second triangle is
Ratio = $3:4$

Note: While calculating the area of triangles if you know that you might have to use the area to find other things like the ratio and lot other things that try not to simplify the answer in the same spot and let it be in the form of fraction so that later on it would be easy for you only to simplify your calculations.