Question

Traingle abc is similar to traingle def such that the area of traingle abc is 36cm and area of traingle def is 49cm then find the ratioof their corresponding sides

Answer 1

Ratio of their corresponding sides is 6:7.

Explanation:

Given:

Area of triangle ABC = 36 square cm

Area of triangle DEF = 49 square cm

Δ ABC
`\sim` Δ DEF

We need to find the ratio of their corresponding sides.

Given that Δ ABC
`\sim` 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;

`\frac{\textrm{Area of Triangle CBA}}{\textrm{Area of Triangle FED}} = (AB^2)/(DE^2)`

Substituting the given values we get;

`(36)/(49)=(AB^2)/(DE^2)`

Now taking square roots on both side we get;

`(√(36))/( √(49))=(√(AB^2))/(√(DE^2))\\\\(6)/(7)=(AB)/(DE)`

Hence Ratio of their corresponding sides is 6:7.