Question

Let triangle ABC similar to triangle DEF area of triangle ABC = to 169 cm square and area of triangle DEF = 121 CM square if ABequals to 26 CM then find DE?

Answer 1

ar (ABC)/ar(DEF)=(AB/DE)^2.

That is, 169/121=(26/DE)^2.

26/DE=13/11.

Therefore DE=26/13×11=22

Answer 2

Answer:

The length of DE is 22 cm

Step-by-step explanation:

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

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.

$\frac{ar(ACB)}{ar(DFE)}=(\frac{AB}{DE})^{2}$

⇒ $\frac{169}{121}=(\frac{26}{DE})^2$

⇒ $\frac{13}{11}=(\frac{26}{DE})^2$

⇒ $DE=\frac{26}{13}\times 11$

⇒ DE=22 cm

The length of DE is 22 cm