Question

29.Areas of two similar triangles are 36 cm2 and 100 cm2. If the length of a side of the larger triangle is 20 cm, then the length of the corresponding side of the smaller triangle is: E. (A) 12cm F. (B) 13cm G. (C) 14cm H. (D) 15cm 30 Afla nalo 10 m high​

Answer 1

$\\ \large\underline{ \green{ \rm \: Answer :-} }$

• Option (A) is correct.

$\\ \rm \underline{\green{ Given }}:- \begin{cases} \sf {Area \: of \: smaller \: \: triangle = 36 {cm}^{2} } \\ \sf Area \: of \: larger \: \: triangle = 100 {cm}^{2} \\ \sf length \: of \: larger \: side \: is \: 20cm \end{cases}$

$\\ \large \underline{\green{ \rm \: To \: find : - }}$

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

$\\ \underline{\large \green{ \rm \: Solution :-} }$

Let's start,

Let the length of smaller triangle's corresponding side be “p”.

So, Using property of“ area of similar triangle”.

$\\ \: \: \: \: \: \: \: \: \: \: \sf \: \frac{Area \: of \: larger \: triangle}{Area \: of \: smaller \: triangle} = \frac{(Side \: of \: larger \: triangle )^{2} }{(Side \: of \: smaller \: triangle ) ^{2} }$

$\\ \sf \: \: \: \: \: \: \implies \: \: \frac{100}{36} = \frac{{(20)}^{2} }{ {p}^{2} }$

$\\ \sf \: \: \: \: \: \: \implies \: \: \frac{100}{36} = \frac{400 }{ {p}^{2} }$

$\\ \sf \: \: \: \: \: \: \implies \: \: {p}^{2} = \frac{400 \times 36}{ 100}$

$\\ \sf \: \: \: \: \: \: \implies \: \: {p}^{2} = {4\times 36}$

$\\ \sf \: \: \: \: \: \: \implies \: \: {p}^{2} = 144$

$\\ \sf \: \: \: \: \: \: \implies \: \: p = \sqrt{144}$

$\\ \sf \: \: \: \: \: \: \implies \: \: \boxed{ \blue{ \frak{ p = 12cm}}}$

Hence, The length of corresponding side of the smaller triangle is 12 cm.