Question

The area of triangle LMN is 18 ft2 and the area of FGH is 24 ft2. If triangle LMN is equivalent to triangle FGH, what is the ratio of LM to FG?
A. 3:4
B. 9:16
C. square root of 3:2
D. 4:3

Answer 1

Answer:  Option 'C' is correct.

Explanation:

Since we have given that

Area of triangle LMN = 18 ft²

Area of triangle FGH = 24 ft²

Since Δ LMN and ΔFGH is equivalent triangles.

As we know the theorem which states that ratio of areas of equivalent triangles is equal to square of ratio of corresponding sides.

So, it becomes,

$\dfrac{\Delta LMN}{\Delta FGH}=(\dfrac{LM}{FG})^2\\\\\dfrac{18}{24}=(\dfrac{LM}{FG})^2\\\\\dfrac{3}{4}=(\dfrac{LM}{FG})^2\\\\\sqrt{\dfrac{3}{4}}=\dfrac{LM}{FG}\\\\\dfrac{\sqrt{3}}{2}=\dfrac{LM}{FG}$

Hence, Option 'C' is correct.

Answer 2

Answer:

Option C

Explanation:

As we know,

Theorem of equivalent triangle states that two similar triangle's area will be proportional to square of corresponding sites.

Thus ,

$\frac{18}{24} = (\frac{LM}{FG} )^2$

On taking square root on both the sides and solving the equation further , we get -

$\sqrt{\frac{18}{24} } = \frac{LM}{FG}\\\frac{LM}{FG} = \sqrt{\frac{3}{4} } \\\frac{LM}{FG} = \frac{\sqrt{3} }{2}$

Thus, option C is correct