Question

The perimeters of two similar triangles ABC and XYZ are 26 cm and 39 cm respectively, then the
ratio of the corresponding medians of two triangles is

Answer 1

If the perimeters of two similar triangles are 26 and 39 cm then the ratio of the corresponding medians of two triangles is 2:3.

Step-by-step explanation:

It is given that,

∆ ABC ~ ∆ XYZ

The perimeter of ∆ ABC = 26 cm

The perimeter of ∆ XYZ = 39 cm  

Let’s assume that the median of ∆ ABC be “AD” and the median of  ∆ XYZ be “XR”.

We know the theorem that the ratio of the areas of the two similar triangles is equal to the square of the perimeter of the corresponding similar triangles as well as square of their corresponding sides.

∴ [Area (Δ ABC)] / [Area (∆ XYZ)] = [Perimeter of ∆ABC]² / [Perimeter of ∆ XYZ]² = [$\frac{AB}{XY}$]²

⇒ [Perimeter of ∆ABC] / [Perimeter of ∆ XYZ]= $\frac{AB}{XY}$

⇒ $\frac{AB}{XY}$ = $\frac{26}{39}$….. (i)  

Also, we know that the ratio of corresponding medians of two similar triangles are equal to the ratio of their corresponding sides of triangles.

∴ $\frac{AD}{XR}$ = $\frac{AB}{XY}$

⇒ $\frac{AD}{XR}$ = $\frac{26}{39}$ ..... [substituting from (i)]

⇒ $\frac{AD}{XR}$ = $\frac{2}{3}$

Thus, the ratio of the corresponding medians of two given similar triangles is 2:3.

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Answer 2

Step-by-step explanation: