Question

Base of a triangle is 12 and height is 10. Base of another triangle is 20 and height is 12. Find the ratio of areas of these triangle​

Answer 1

Given:

• Base of 1st Triangle = 12 units
• Height of 1st Triangle = 10 units
• Base of 2nd Triangle = 20 units
• Height of 2nd Triangle = 12 units

Find:

• Ratio of the Area of both Triangles

Solution:

For f1st Triangle

we, know that

$\boxed{ \sf Area \: of \: triangle = \dfrac{1}{2} \times b \times h}$

where,

• Base, b = 12 units
• Height, h = 10 units

So,

$\dashrightarrow \sf Area \: of \: triangle_{1} = \dfrac{1}{2} \times b \times h$

$\dashrightarrow \sf Area \: of \: triangle_{1} = \dfrac{1}{2} \times 12 \times 10$

$\dashrightarrow \sf Area \: of \: triangle_{1} = \dfrac{1}{2} \times 120$

$\dashrightarrow \sf Area \: of \: triangle_{1} = \dfrac{120}{2}$

$\dashrightarrow \sf Area \: of \: triangle_{1} = 60 \: sq. \: units$

$\therefore \sf Area \: of \: triangle_{1} = 60 \: sq. \: units$

$\rule{300}{2}$

For 2nd Triangle

Again using

$\boxed{ \sf Area \: of \: triangle = \dfrac{1}{2} \times b \times h}$

where,

• Base, b = 20 units
• Height, h = 12 units

So,

$\dashrightarrow \sf Area \: of \: triangle_{2} = \dfrac{1}{2} \times b \times h$

$\dashrightarrow \sf Area \: of \: triangle_{2} = \dfrac{1}{2} \times 20 \times 12$

$\dashrightarrow \sf Area \: of \: triangle_{2} = \dfrac{1}{2} \times 240$

$\dashrightarrow \sf Area \: of \: triangle_{2} = \dfrac{240}{2}$

$\dashrightarrow \sf Area \: of \: triangle_{2} = 120 \: sq. \: units$

$\therefore\sf Area \: of \: triangle_{2} = 120 \: sq. \: units$

$\rule{300}{2}$

Now,

$\sf :\to Ratio \: of \: area \: of \: triangle = \dfrac{Area \: of \: triangle_{1}}{Area \: of \: triangle_{2}}$

where,

• Area of triangle $_1$ = 60 sq. units
• Area of Triangle $_2$ = 120 sq. units

So,

$\sf :\to Ratio \: of \: area \: of \: triangle = \dfrac{Area \: of \: triangle_{1}}{Area \: of \: triangle_{2}}$

$\sf :\to Ratio \: of \: area \: of \: triangle = \dfrac{60}{120}$

$\sf :\to Ratio \: of \: area \: of \: triangle = \dfrac{6}{12}$

$\sf :\to Ratio \: of \: area \: of \: triangle = \dfrac{1}{2}$

Hence, Ratio of Area of both Triangles = 1:2