Question

areas of two similar triangles is 360cm and 250cm respectively one side of the first triangle is 8cm find the length of corresponding side of second triangle​

Answer 1

Step-by-step explanation:

Let the bigger ∆ be ∆ABC and smaller be ∆XYZ

and let corresponding sides be AB and XY resp.

A(∆ABC) : A(∆XYZ) = 360 : 250

By the theorem of area of. similar triangles

(AB)²/(XY)². = 360 : 250 = 36/25

Taking Square root

AB/XY = 6/5

now we know that AB = 8 cm

8/XY = 6/5

XY = 8/6 X 5

XY = 40/6 = 20/3 = 6.66 cm

Therefore length of corresponding side of other triangle is 6.66 cm

Answer 2

Answer:

6.67 cm

Step-by-step explanation:

$\rule{200}2$

▶ Theorem Used

The ratio of the areas of two similar triangle is equal to the square of the ratio of their corresponding sides.

Given

→Area of two similar triangles are 360 cm² and 250 cm² respectively

→ One side of the first triangle is 8 cm

To find

Length of the corresponding side of second triangle

Solution

Let,

length of corresponding side of second triangle be x

then,

Using the area theorem

$\implies\sf{\frac{360}{250}=\left(\frac{8}{x}\right)^2}$

$\implies\sf{\frac{36}{25}=\frac{64}{x^2}}$

$\implies\sf{x^2=\frac{64\times25}{36}}$

$\implies\boxed{\sf{x=6.67\;cm \;(approx.)}}$  

$\rule{200}2$