Question

areas of two similar triangles are 36 cm2 and 100 cm2 , if the length of a side of tje larger triangle is 20cm find the length of the corresponding side of the smaller triangle​

Answer 1

Step-by-step explanation:

Given :-

• Areas of two similar triangles are 36 cm² and 100 cm² .
• The length of a side of the larger triangle is 20 cm .

To find :-

• Find the length of the corresponding side of the smaller triangle .

Concept used :-

• If two triangles are similar then the ratio of areas of the two triangles is proportional to ratio of square of their corresponding sides .

Solution :-

area of first triangle = 36 cm²

area of second triangle = 100 cm² .

$\sf \: ratio \: of \: the \:areas \: = \dfrac{36}{100}$

$\sf \: ratios \: of \: the \: sides \: = \dfrac{ {(side)}^{2} }{ {(20)}^{2} }$

According to Theorem :- If two triangles are similar then the ratio of areas of the two triangles is proportional to ratio of square of their corresponding sides .

Then,

$\sf \dfrac{36}{100} = \dfrac{ {(side)}^{2} }{ {(20)}^{2} } \\ \\ \sf \: \frac{36}{100} = \frac{ {side}^{2} }{400} \\ \\ \sf 100 \times {side}^{2} = 14400 \\ \\ \sf {side}^{2} = \frac{144 \cancel{00}}{1 \cancel{00 }} \\ \\ \sf \: {side}^{2} = 144 \\ \\ \sf \: side = \sqrt{144} \\ \\ \boxed{ \sf side \: = 12 \: cm \: }$

Hence, side = 12 cm