The area of two similar triangles are 9 sq m and 36 sq m , respectively. If the height of one triangle is 24 m , then the height of the other one is

Correct option is A

Given:

Areas of two similar triangles = 9 sq m and 36 sq m

Height of smaller triangle = 24 m

Concept Used:
In similar triangles, the ratio of the areas is equal to the square of the ratio of their corresponding sides (including height).

Formula Used:

​$$\frac{\text{Area}_1}{\text{Area}_2} = \left( \frac{\text{Height}_1}{\text{Height}_2} \right)^2$$​​

Solution:
Let the unknown height be h

​$$\frac{9}{36} = \left( \frac{24}{h} \right)^2 \\ \ \\ \frac{1}{4} = \left( \frac{24}{h} \right)^2\\ \ \\ \sqrt{\frac{1}{4}} = \frac{24}{h} \\ \ \\ \frac{1}{2} = \frac{24}{h}\\ \ \\ \implies h = 48 \ m$$​​