Question

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

Answer 1

Given :

• Base of 1st Triangle = 9
• Height of Triangle = 5
• Base of 2nd Triangle = 10
• Height of Triangle = 6

To Find :

• Find the Ratio of Areas

$\\ \qquad{\rule{200pt}{2pt}}$

SolutioN :

$\dag$ Formula Used :

${\qquad \; {\green{\bigstar \; \; {\purple{\underbrace{\underline{\red{\sf{ Area{\small_{(Triangle)}} = \dfrac{1}{2} \times Base \times Height }}}}}}}}}$

$\dag$ Calculating the Ratio :

$\begin{gathered} \qquad :\longmapsto \; \; \sf { Ratio = \dfrac{ Area_1 }{ Area_2 } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad :\longmapsto \; \; \sf { Ratio = \dfrac{ \dfrac{1}{2} \times Base \times Height }{ \dfrac{1}{2} \times Base \times Height } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad :\longmapsto \; \; \sf { Ratio = \dfrac{ \dfrac{1}{2} \times 9 \times 5 }{ \dfrac{1}{2} \times 10 \times 6 } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad :\longmapsto \; \; \sf { Ratio = \dfrac{ \dfrac{1}{2} \times 45 }{ \dfrac{1}{2} \times 60 } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad :\longmapsto \; \; \sf { Ratio = \dfrac{ \dfrac{45}{2} }{ \dfrac{60}{2} } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad :\longmapsto \; \; \sf { Ratio = \dfrac{ \cancel\dfrac{45}{2} }{ \cancel\dfrac{60}{2} } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad :\longmapsto \; \; \sf { Ratio = \dfrac{ 22.5 }{ 30 } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad :\longmapsto \; \; \sf { Ratio = \cancel\dfrac{ 22.5 }{ 30 } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad :\longmapsto \; \; \sf { Ratio = \dfrac{ 3 }{ 4 } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad :\longmapsto \; \; {\underline{\boxed{\pmb{\sf { Ratio = 3:4 }}}}} \; {\purple{\pmb{\bigstar}}} \\ \\ \\ \end{gathered}$

$\therefore \;$ The Ratio of the Areas is 3:4 .

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Answer 2

Given:-

• Two triangles of dimensions
• Base=9 and 10 respectively.
• Height= 5 and 6 respectively.

To find:-

• Ratio of their areas

Solution:-

★We can calculate the areas of the figure and the divide the numbers till the lowest form to find it's ratio of the areas. The formula for calculating area of a triangle is given below★

$\large \blue{\underline{ \green{\boxed{\bf{ \red{ \: \: \: \: \: \: \implies \frac{1}{2} \times b \times h \: \: \: \: \: \: }}}}}}$

»Where,

• b=base of the triangle.
• h=height of the triangle.

★Now, on substituting values we get:-

Calculating for 1st triangle:-

$\large\underline{\sf{ \implies\frac{1}{2} \times 9 \times 5}}$

$\large\underline{\sf{ \implies9 \times 2.5}}$

$\large \green{\underline{ \boxed{\sf{ \red{ \: \: \: \: \: \: \: \: \: \: \: \: \implies22.5 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:}}}}}$

Calculating for 2nd triangle:-

$\large\underline{\sf{ \implies \frac{1}{2} \times 10 \times 6 }}$

$\large\underline{\sf{ \implies5 \times 6}}$

$\large \blue{\underline{ \green{ \boxed{{\sf{ \red{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies30 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }}}}}}}$

Now we will simply them:-

$\large\underline{\sf{ \implies\frac{22.5}{30} }}$

$\large \blue{\underline{ \green{ \boxed{\sf{ \red{ \: \: \: \: \: \: \: \: \: \: \implies1.5 \ratio30 \: \: \: \: \: \: \: \: \: \: \: \: \: }}}}}}$

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Basic concept!!

• A triangle is a 2-D figure.
• It is of 3 types.

1. Equilateral triangle
2. Isosceles triangle
3. Scalene triangle

• There are 3 different formulas to calculate.

1. For equilateral triangle:- √3/4. ×s²
2. For isosceles triangle:- 1/2 ×b×h
3. For scalene triangle:- √s(s-a)(s-b)(s-c)

• In equilateral triangle all sides and angles are equal.
• In isosceles triangle two sides and two angles are equal.
• In scalene triangle all sides and angles are uneven and different.