Question

lf the areas of two similar triangles are 9:25 then their corresponding sides are is the ration​

Answer 1

$\huge\text{\underline{Answer}}$

$\bold\red{AB : DE = 3 : 5}$

$\sf{\underline{Explanation }}$

Let the △ABC and △DEF are two triangles .

Such that ,

△ABC ~ △DEF

Then, according to theorm,

The area of two similar triangle are in the same ratio as its square of the corresponding side.

ar ( △ABC) : ar ( △DEF) = 9 : 25

Now according to theorm,

$\frac{ar ABC}{ar DEF} = \frac{ {AB}^{2} }{ {DE}^{2} }$

$\implies$ $\bold{</strong><strong>\frac{9}{25} = \frac{ {</strong><strong>AB</strong><strong>}^{2} }{ {</strong><strong>DE</strong><strong>}^{2} } </strong><strong>}$

$\implies$ $\bold{</strong><strong>\frac{3}{5} = \frac{</strong><strong>A</strong><strong>B</strong><strong>}{</strong><strong>A</strong><strong>C</strong><strong>} </strong><strong> }$

$\implies$ $\bold</strong><strong>\</strong><strong>r</strong><strong>e</strong><strong>d</strong><strong>{</strong><strong>A</strong><strong>B</strong><strong> </strong><strong>:</strong><strong> </strong><strong>BC</strong><strong> </strong><strong>=</strong><strong> </strong><strong>3</strong><strong> </strong><strong>:</strong><strong> </strong><strong>5</strong><strong>}$

hence, the ratio of corresponding sides are in 3: 5 .

Answer 2

Answer:

3:5

Step-by-step explanation:

The ratio of areas of two triangles of two similar triangles having areas A1 and A2 respectively is given by

A1/A2 = (S1/S2)²

9/25 = (S1/S2)²

Taking square root on both the sides we get,

✓(S1/S2)² = ✓(9/25)²

S1/S2 = 3/5

The ratio of their corresponding sides will be

S1:S2 = 3:5