Question

Areas of two similar triangles are 100 and 64 if the length of the median of a big triangle is 10 then the median of smaller triangle is​

Answer 1

SoluTion :-

Given area of two similar triangles are 100 sq cm and 64 sq cm

The areas of two Similar-Triangles are in the ratio of the squares of the corresponding medians

$\sf {The\ ratio\ of\ area\ of\ triangle=\frac{100}{64} = \frac{25}{16} }$

Median of greater triangle is 13 cm and let other median is x cm

$\sf{\Therefore \frac{(13)^2}{(x)^2}=\frac{25}{16} }\\\\\\\sf {\Rightarrow \frac{169}{x^2} = \frac{25}{16} }\\\\\sf {x^2 = \frac{169 \times 16}{25}=108.16 }\\\\\sf {x=10\ cm}$

Answer 2

Answer:

the midean of smaller triangle is 8

Step-by-step explanation:

given

area of two similar triangle is 100 and 64

so let area of ∆ABC =100

and area of∆DEF =64

so

area of∆ABC/area of∆DEF =100/64

so we know that when two triangle is similar then their sides are in proportion and also Midian are in proportion

let in traingle ABC the Midian is AG and in DEF median is DH

so area of∆ABC/area of∆DEF =AB/DE=BC/EF = AG/DH

so 10/8=10/DH

so DH =8