Question

The ratio of the areas of two triangles with the same height is 2:3. If the height of the smaller triangle is 3.6 cm find the height of the bigger triangle.​

Answer 1

$\mathtt{\huge{\underline{\red{Answer\: :}}}}$

Given :

Ratio of height = 2 : 3

Height of smaller triangle = 3.6 cm.

According to the question :

Let ' x1 ' and ' x2 ' be the areas of two triangles.

☞ x1 = 1 / 2 × b1 × h1

☞ x2 = 1 / 2 × b2 × h2

=> x1 / x2 = 1/2 × b1 × h2 / 1/2 × b2 × h2

=> 2 / 3 = b1 × h1 / b2 × h2

☞ h1 / h2 = 2 / 3 ( h1 = 3.6 cm )

Equation :

=> 3.6 / h2 = 2 / 3 ( cross multiply )

=> h2 = 3.6 × 3 / 2

=> h2 = 5.4 cm.

$<marquee><b><font colour="red">$Therefore, The height of the bigger triangle is 5.4 cm ☺❄☺