Answer :
Answer:
Ratio of their corresponding sides is 6:7.
Step-by-step explanation:
Given:
Area of triangle ABC = 36 square cm
Area of triangle DEF = 49 square cm
Δ ABC [tex]\sim[/tex] Δ DEF
We need to find the ratio of their corresponding sides.
Given that Δ ABC [tex]\sim[/tex] Δ DEF
So we can say that by Triangle Similarity property which states;
"When two triangles are similar then the ratio of their Area is equal to ratio of square of the corresponding sides."
framing in equation form we get;
[tex]\frac{\textrm{Area of Triangle CBA}}{\textrm{Area of Triangle FED}} = \frac{AB^2}{DE^2}[/tex]
Substituting the given values we get;
[tex]\frac{36}{49}=\frac{AB^2}{DE^2}[/tex]
Now taking square roots on both side we get;
[tex]\frac{\sqrt{36}}{ \sqrt{49}}=\frac{\sqrt{AB^2}}{\sqrt{DE^2}}\\\\\frac{6}{7}=\frac{AB}{DE}[/tex]
Hence Ratio of their corresponding sides is 6:7.