Question

The areas of two similar triangles are 12 and 48. if the height of smaller one is 2.1 then find corresponding height of bigger triangle

Answer 1

"Given,

Area of two similar triangles = 12 cm², 48 cm².

Area of bigger triangle = 48 cm²

Area of smaller triangle = 12 cm²

We know that, Ratio of the areas of two similar is equal to square of the ratio of corresponding heights or altitudes.

Given, Height of smaller triangle =2.1 cm.

Area (Bigger Triangle)/Area (Smaller Triangle) = (Height of bigger triangle) ^2/ (Height of smaller triangle) ^2

48/12 = (Height of bigger triangle) ^2/2.1²

4 = (Height of the triangle) ² / 4.41

√ (4 * 4.41) = Height of the bigger triangle

Height of the bigger triangle = 2 * 2.1 = 4.2 cm.

"

Answer 2

Step-by-step explanation:

Hey there!

Given,

Area of two similar triangles = 12 cm² , 48 cm² .

Area of bigger triangle = 48 cm²

Area of smaller triangle = 12 cm²

We know that, Ratio of the areas of two similar is equal to square of the ratio of corresponding heights or altitudes.

Given, Height of smaller triangle =2.1 cm.

\boxed{\frac{ Ar(Bigger \: triangle)}{Ar(Smaller \: triangle)} = ( \frac{ Height \: of \: bigger \: triangle } {Height \: of \: smaller \: triangle } )^2}Ar(Smallertriangle)Ar(Biggertriangle)=(HeightofsmallertriangleHeightofbiggertriangle)2

\implies \frac{ 48}{12} = \frac{(Height \: of \: bigger \: triangle)^2 } { 2.1^{2}}⟹1248=2.12(Heightofbiggertriangle)2

4 = (Height of the triangle)² / 4.41

√(4 * 4.41) = Height of the bigger triangle

Height of the bigger triangle = 2 * 2.1 = 4.2 cm.