Question

10)
The area of two similar triangles are a and k'a. The ratio of the
corresponding sides of the triangles is ....
A box has 10 equal
11)
size​

Answer 1

Step-by-step explanation:

here is the ans it is √a/√k'a

solved by theorem of areas of similar triangle

Answer 2

Answer:

The ratio of corresponding sides of triangle is $\sqrt{a} : \sqrt{k'a}$

Step-by-step explanation:

Given:

The area of triangle 1 (ΔT₁) = a

The area of triangle 2 (ΔT₂) = k'a

To find:

The ratio of corresponding sides of the triangle.

Formula:

Consider two similar triangles ΔABC and ΔPQR,

$\frac{Area of triangle ABC}{Area of triangle PQR} = (\frac{AB}{PQ} )^{2} = (\frac{BC}{QR}) ^{2} = (\frac{CA}{RP} )^{2}$

$Area of triangle = \frac{1}{2}*Base*Height$

Solution:

$\frac{A(T_{1}) }{A(T_{2} )} = \frac{A(T_{1} ^{2}) }{A(T_{2} ^{2}) }\\ \\= \frac{a^{2} }{(k'a)^{2} }\\ \\= \frac{\sqrt{a} }{\sqrt{k'a} }$

The area of similar triangle theorem states that "If the area of two triangles are similar then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides".

The ratio of sides of triangle = $\sqrt{a}$ : $\sqrt{k'a}$

#SPJ3