Question

the ratio of the areas of two similar triangles is 1:4 then the ratio of there corresponding sides​

Answer 1

Answer:

1/2

Step-by-step explanation:

The ratio of area of two similar triangle = Ratio of square of corresponding side.

so ratio of corresponding sides = root( Ratio of area of two triangles) = root1/root4 = 1/2 =1:2

Answer 2

Given:

the ratio of the areas of two similar triangles is 1:4

To Find:

the ratio of their corresponding sides​

Solution:

It is given that the ratio of the area of two similar triangles is 1:4 then we need to find the ratio of their corresponding sides, in basic words and logically it is said that if two triangles have a ratio of areas as a/b then the ratio of their sides will be the square root of their ratio of areas. We can also derive it and find the value for this sum,

Let us take two similar triangles which are right angled triangles and their base and height is the same 'a1' and 'a2' and we also the formula for the area of a right angled triangle that is

$A=\frac{1}{2} *b*h$

Now using the given ratio and applying the value we get,

$\frac{\frac{1}{2} *a_{1}^2}{\frac{1}{2} *a_{2}^2} =\frac{1}{4}\\\frac{a_{1}}{a_{2}} =\frac{1}{2}$

We can see that we did the square root of the ratio of area to find the ratio of sides.

Hence, the ratio of sides is 1:2.