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 area of the triangles​

Answer 1

Given:

✰ Base of one triangle = 9 units

✰ Height of one triangle = 5 units

✰ Base of another triangle = 10 units

✰ Height of another triangle = 6 units

To find:

✠ The ratio of area of the triangles.

Solution:

Here in this question! First we will find the area of first triangle by using formula. Then, we will find the area of another triangle. ( Putting the values in the formula and doing the required calculations ). After that, we will find the ratio of area of these triangles.

✭ Area of a triangle = 1/2 × b × h ✭

Where,

• b is the base of a triangle.
• h is the corresponding height of a triangle.

Putting the values in the formula, we have:

➛ Area of one triangle = 1/2 × 9 × 5

➛ Area of one triangle = 1/2 × 45

➛ Area of one triangle = 45/2

➛ Area of another triangle = 1/2 × 10 × 6

➛ Area of another triangle = 1/2 × 60

➛ Area of another triangle = 60/2

Now,

➤ Ratio of areas of the triangles = 45/2/60/2

➤ Ratio of areas of the triangles = 45/2 × 2/60

➤ Ratio of areas of the triangles = 45/60

➤ Ratio of areas of the triangles = 9/12

➤ Ratio of areas of the triangles = 3/4

➤ Ratio of areas of the triangles = 3:4

∴ The ratio of area of the triangles = 3:4

_______________________________

Answer 2

Given :

• Base of Triangle (1) = 9 units
• Height of Triangle (1) = 5 units
• Base of Triangle (2) = 10 units
• Height of Triangle (2) = 6 units

To find :

• The ratio of the areas of both the triangles

Solution :

• $\sf{Area~of~a~triangle={\dfrac{1}{2}}×b×h}$

Area of Triangle (1)

• Base = 9 units
• Height = 5 units

$\sf\implies{{\dfrac{1}{2}}×9×5}$

$\sf\implies{{\dfrac{1}{2}}×45}$

$\sf\implies{{\blue{\underline{\boxed{\sf{\pmb{~{\dfrac{45}{2}}~}}}}}}}$

Area of Triangle (2)

• Base = 10 units
• Height = 6 units

$\sf\implies{{\dfrac{1}{2}}×10×6}$

$\sf\implies{{\dfrac{1}{2}}×60}$

$\sf\implies{{\blue{\underline{\boxed{\sf{\pmb{~{\dfrac{60}{2}}~}}}}}}}$

Ratio :

$\sf{~~Area~of~Triangle~(1):Area~of~Triangle~(2)}$

$\sf{~~~~~~~~~~={\dfrac{45}{2}}:{\dfrac{60}{2}}}$

$\sf ~~~~~~~~~~= \dfrac{ (\frac{45}{2} )}{ (\frac{60}{2} )}$

$\sf{~~~~~~~~~~= {\dfrac{45}{2}}÷{\dfrac{60}{2}}}$

$\sf{~~~~~~~~~~= {\dfrac{45}{\cancel{~2~}}}×{\dfrac{\cancel{~2~}}{60}}~~~~~~~~(reciprocal)}$

$\sf{~~~~~~~~~~= {\dfrac{45}{60}}}$

$\sf{~~~~~~~~~~= {\dfrac{3}{4}}~~~~~~~~(common~factor=15)}$

$\sf{~~~~~~~~~~\therefore {\underline{\boxed{\sf{\pmb{Ratio=3:4}}}}}}$

∴ Required answer :

$\blue{ \underline{ \underline{ \sf{Area~of~Triangle~(1):Area~of~Triangle~(2) = { \pmb{3:4}}}}}}$