Question

sides of two similar triangles are in the ratio 4:9 Areas of these triangles are in the ratio
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Answer 1

Answer:

Areas of these triangles are in the ratio $16:81.$

Step-by-step explanation:

Sides of two similar triangles are in the ratio $4:9.$

Let us consider the sides of the similar triangle be $4x$ and $9x$  respectively.

The formula to find the area of a triangle be given by:-

Area of a equilateral triangle =$\frac{\sqrt{3} }{4}\hspace{2mm}l^2$

Area of the first triangle =

                                       $\frac{\sqrt{3} }{4}\hspace {2mm} (4x)^2\\ \\ =\frac{\sqrt{3} }{4}\hspace {2mm} (16x^2)\\ \\ =4\sqrt{3}x^2 ----(1)$

Area of the second triangle =

                                             $\frac{\sqrt{3} }{4}\hspace{2mm}(9x)^2\\ \\= \frac{\sqrt{3} }{4}\hspace{2mm}81x^2----(2)$

The ratio of area between the two triangle be

                                             $\frac{16}{81}$

The ratio is in ratio 16:81.