Question

12. 360 sq. cm and 250 sq. cm are the ar
me areas of two similar triangles. If the length of one of the sides of the
first triangle be 8 cm, then the length of the corresponding side of the second trany
(a) 6 cm
(b)6 5 cm (c)65 cm (d)6 cm (e) None of these

​

Answer 1

||✪✪ QUESTION ✪✪||

360 sq. cm and 250 sq. cm are the areas of two similar triangles. If the length of one of the sides of the first triangle be 8 cm, then the length of the corresponding side of the second triangle is :-

(a) 6 cm (b)6 5 cm (c)65 cm (d)6 cm (e) None of these

|| ★★ FORMULA USED ★★ ||

→ If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides.

Let us assume that ∆ABC is Similar to ∆PQR,

Than, we can say that :-

→ (Area ∆ABC) / (Area ∆PQR) = (AB/PQ)² = (BC/QR)² = (CA/RP)².

|| ✰✰ ANSWER ✰✰ ||

Given , that, Two Similar ∆'s have area 360cm² and 250cm² and Length of First ∆ is 8cm.

Let us assume that, side of another ∆ is x cm.

So, we can say that :-

→ (360/250) = (8)² / (x)²

→ 36/25 = 64/x²

→ x² = (25*64) / 36

→ x = (5 * 8) /6

→ x = 6.67cm. (E)

Hence, Length of Another Similar ∆ is 6.67cm. Option (E). None of These.

Answer 2

$\huge \boxed{ \fcolorbox{cyan}{grey}{Answer : }}$

here..

the ratios of the corresponding sides of similar traingles is equal to the square of the root of the ratio of their areas...

$\sf{given}$

$\rm{area \: are \: 360 \: and \: 250 \: square \: units}$

then

the ratio area is

$\sf{ \frac{360}{250}} = \frac{36}{25}$

the ratio of corresponding sides is

$\sf{ \sqrt{36 \div 25} = \frac{6}{5}}$

given that sides is 8 unit(larger triangle)

$\sf{smaller \: triangle \: is \: 8 \times \frac{5}{6} = \frac{20}{3}}$

corresponding side of the triangle⤴

option is none of these..

the ratio of the areas of the two similar triangle is equal to the square of the root of ratio of their areas