Question

∆ABC~∆DEF bc=3.5cm and ef=2.5cm then area of ∆ABC=9cm² then area of ∆def is________approximately.​

Answer 1

Step-by-step explanation:

Given that:∆ABC~∆DEF bc=3.5cm and ef=2.5cm then area of ∆ABC=9cm²

To find:area of ∆def is________approximately.

Solution:

Tip: We know that if two triangles are similar then ratios of squares of corresponding sides is equal to ratios of areas.

i.e.

$\frac{( {BC)}^{2} }{( {EF)}^{2} } = \frac{ar( \triangle \: ABC)}{ar( \triangle \: DEF)}$

Here BC=3.5 cm

EF=2.5 cm

ar(∆ABC)= 9 cm²

Apply these values in the thrown in order to find the area of ∆DEF

$\frac{( {3.5)}^{2} }{( {2.5)}^{2} } = \frac{9}{ar( \triangle \: DEF)} \\ \\ \frac{( {35)}^{2} }{( {25)}^{2} } = \frac{9}{ar( \triangle \: DEF)} \\ \\ \frac{( {7)}^{2} }{( {5)}^{2} } = \frac{9}{ar( \triangle \: DEF)} \\ \\ \frac{49 }{25 } = \frac{9}{ar( \triangle \: DEF)} \\ \\ ar( \triangle \: DEF) = \frac{9 \times 25}{49} \\ \\ ar( \triangle \: DEF) = \frac{225}{49} \\ \\ ar( \triangle \: DEF) =4.59 cm^2$

Thus, area of triangle DEF=4.59 cm²

hope it helps you.

To learn more in brainly:

1)∆abc~∆def if ab=4cm,bc=3.5cm,ca=2.5cm and df=7.5cm find the perimeter of ∆def

https://brainly.in/question/2746515

Answer 2

ar(△DEF)=4.59cm ........