Two sides and the perimeter of one triangle are respectively three times the corresponding sides and the perimeter of other - Maths - Triangles

Question

Two sides and the perimeter of one triangle are respectively
three times the corresponding sides and the perimeter of other
triangle Are the two triangles similar ? Why ? PLEASE EXPLAIN IN
DETAIL

Santosh Kumar · Accepted Answer

Let the sides of the first triangle be a, b and x.

Then, corresponding sides of the other triangle are 3a, 3b and y (let) respectively.

Perimeter of the first triangle,

P₁ = a + b + x

Perimeter of the second triangle,

P₂ = 3a + 3b + y

Now,

P₂ = 3P₁

$\Rightarrow 3 a + 3 b + y = 3 (a + b + x) \Rightarrow y = 3 x As, \frac{AB}{DE} = \frac{AC}{DF} = \frac{BC}{EF} = \frac{1}{3} ∴ Δ ABC \sim Δ DEF (sss)$

Two sides and the perimeter of one triangle are respectively three times the corresponding sides and the perimeter of other triangle. Are the two triangles similar ? Why ? PLEASE EXPLAIN IN DETAIL