Question

The altitudes of two similar triangles are 4cm and 6cm. If the area of one triangle is 36 square cm, What is the area of the other?​

Answer 1

Answer:

✡81cm²☑

Step-by-step explanation:

Given⤵

• The altitudes of two similar triangles are 4cm and 6cm.
• The area of one triangle is 36 square cm.

To find⤵

• Area of other triangle.

Solution⤵

⚫Using area of similar triangle theorem:-

"The ratio of the areas of two similar triangles is equal to the square of the ratio of any pair of their corresponding sides".

⚫Here the corresponding sides are 4cm and 6cm .

Hence the ratio is 4cm/6cm= 2/3

⚫Here one triangle areas is 36cm².

✡By area of similar triangle theorem .

➡Let the other triangle area is x.

Therefore,

$\frac{36}{x}=(\frac{2}{3})²$

$\frac{36}{x}=\frac{4}{9}$

By Crossing multiplication

$4x=36×9$

$x=\frac{36×9}{4}$

➡81cm²

✅Hence,the area of other triangle also 81cm².

Extra points⤵

Similar triangle area theorem⤵

"The ratio of the areas of two similar triangles is equal to the square of the ratio of any pair of their corresponding sides".

✍akashbindjnvg✍

Hope this is helpful to you!