Question

The areas of two similar triangles are 196cm² and 169cm²,if the median of first triangle is 4cm then median of other triangle is

Answer 1

Answer:

3.25

Step-by-step explanation:

Ar(1st triangle)/Ar(2nd triangle)

= (median of 1st triangle)²/(median of 2nd triangle)²

=> 196 cm²/169 cm² = 4²/((median of 2nd triangle)²)²

=> (16/13)² = (4/median of 2nd triangle)²

=> 16/13 = 4/median of 2nd triangle

=> median of 2nd triangle = 13×4/16 = 13/4 = 3.25.

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Answer 2

Median of the second triangle is 3.71 cm.

Step-by-step explanation:

Given:

Area of one triangle $A_1$ = $196\ cm^2$

Area of second triangle $A_2$ = $169 \ cm^2$

Median of one triangle $m_1 = 4\ cm$

We need to find the median of the second triangle $m_2$.

Solution:

Now we know that;

When 2 triangle are similar then their ratios of Area are equal to square of the ratio of the medians.

framing in equation form we get;

$\frac{A_1}{A_2}=\frac{(m_1)^2}{(m_2)^2}$

Substituting the values we get;

$\frac{196}{169}=(\frac{4}{m_2})^2$

$(\frac{14}{13})^2=(\frac{4}{m_2})^2$

Taking square root on both side we get;

$\sqrt{(\frac{14}{13})^2}=\sqrt{(\frac{4}{m_2})^2}\\\\\frac{14}{13}=\frac{4}{m_2}$

Now By Cross Multiplication we get;

$m_2=\frac{4\times13}{14} = 3.71\ cm$

Hence Median of the second triangle is 3.71 cm.