Question

let triangle ABC ~ triangle DEF , area(Triangle ABC)=169cm2 and Area( triangle DEF)= 121 cm2 .If AB=26 cm then find DE​

Answer 1

As the triangles are similar  

ar(ABC)/ar(DEF)=AB/DE

root(169/121)=26/DE   ( we took root of area because area is  side *side )

13/11=26/DE

DE=26*11/13

    =22cm

Answer 2

Answer:

The length of DE is 22 cm

Step-by-step explanation:

$\sf \: Given \triangle \: ABC \: similar \: to \triangle \: DEF \: \: and \: ar(ABC)=169cm^2 \: and \\ \sf \: ar(DFE) = 121cm^2$

also AB=26 cm

If ΔABC and ΔDEF are similar then by similar triangle theorem which states that if two triangles are similar then ration of their areas is the square of the ratio of their sides.

$\sf \frac{ar(ACB)}{ar(DFE)}= \bigg(\frac{AB}{DE} \bigg)^{2} \\ \\ \sf \: ⇒ \frac{169}{121}= \bigg(\frac{26}{DE} \bigg)^2 \\ \\ \sf⇒ \frac{13}{11}= \bigg(\frac{26}{DE} \bigg)^2 \\ \\ \sf⇒ DE=\frac{26}{13}\times 11$

$\longrightarrow \sf \: DE=22 cm$

The length of DE is 22 cm