Question

The area of two similar triangles ABC and DEF are 64cm2 and 169cm2 respectively.If the length of BC is 4cm,find the length of EF.(with diagram)

Answer 1

here is your answer shivangi Gautam by Sujeet,,,

Answer 2

Answer: 6.5 cm

Step-by-step explanation:

Given : The area of two similar triangles ABC and DEF are 64 $cm^2$ and 169 $cm^2$ and respectively.

We know that if two triangles area similar then their corresponding sides are proportional.

Since, ΔABC≈ΔDEF

Therefore, $\frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{DF}$

Also, the ration of area of similar triangles is equal to the square of the ratio of the  corresponding sides.

Therefore, we get

$\frac{\text{arABC}}{arDEE}=(\frac{BC}{EF})^2\\\Rightarrow\frac{64}{169}=\frac{4^2}{EF^2}\\\Rightarrow\ EF^2=\frac{16\times169}{64}\\\Rightarrow\ EF^2=\frac{169}{4}\\\Rightarrow\ EF=\frac{13}{2}=6.5$

Hence,  the length of EF = 6.5 cm.