Question

The areas of two similar triangles are 169 cm² and 121 cm² respectively. If the longest side of the larger triangle is 26 cm, what is the length of the longest side of the smaller triangle?

Answer 1

||✪✪ QUESTION ✪✪||

The areas of two similar triangles are 169 cm² and 121 cm² respectively. If the longest side of the larger triangle is 26 cm, what is the length of the longest side of the smaller triangle ?

|| ★★ 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 169cm² and 121cm² and Length of longest side of First ∆ is 26cm.

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

So, we can say that :-

→ (169/121) = (26)² / (x)²

→ 169/121 = (26/x)²

→ (13/11)² = (26/x)²

Square - Root both sides ,

→ (13/11) = (26/x)

Cross - Multiplying,

→ 13x = 11 * 26

→ x = (11 * 26) /13

→ x = 22 cm.

Hence, Length of longest sides of Another Similar ∆ is 22cm.

Answer 2

Question

The areas of two similar triangles are 169 cm² and 121 cm² respectively. If the longest side of the larger triangle is 26 cm, what is the length of the longest side of the smaller triangle?

Solution

Let $\sf A_1$ and $\sf \ A_2$ be the areas of the triangles whose areas are 169 cm² and 121 cm² respectively.

• The longest side of $\sf A_1$ is 26 cm

• Both the triangle are similar to eachother

Let the unknown side of $\sf A_2$ be K

Now,

The ratio of areas of two similar triangles is equal to the ratio of the square of their corresponding sides

$\boxed{\boxed{\sf \dfrac{A_1}{A_2} = \dfrac{26^2}{K^2}}}$

$\implies \: \sf \dfrac{169}{121} = \dfrac{ {26}^{2} }{ {K}^{2} } \\ \\ \implies \ \sf \: \dfrac{ {13}^{2} }{ {11}^{2} } = \dfrac{26 {}^{2} }{ {K}^{2} } \\ \\ \implies \: \sf \: {K}^{2} = \sqrt{ {11}^{2} \times {2}^{2} } \\ \\ \implies \: \boxed{ \boxed{ \sf \: K = 22 \: cm}}$

The unknown side of the triangle would be 22 cm