Question

40 POINTS PLS HELP I WILL ALSO GIVE BRAINLY (ANSWER THE BOXES ON BOTTOM RIGHT)

Answer 1

Answer: See explanation

Step-by-step explanation:

ΔLNM and ΔLKN are 30°- 60°- 90° triangles

We have to find the length of LN before we can find the length of MN.

In a 30°- 60°- 90° triangle, the length of the hypotenuse is 2 times the length of the shorter leg, and the length of the longer leg is the length of the shorter leg times √3

Since the hypotenuse is 6, the short leg would be 3 since the hypotenuse is 2 times the length of the short leg.

LN = √3 times the shorter leg

3 × √3 = 3√3

LN = 3√3

We now know the length of the longer leg in ΔLNM (3√3)

MN would be 3√3 × √3

3√3 × √3

= 3√9

= 3 × 3 = 9

MN = 9

ΔLKM is also a 30° - 60° - 90° triangle

The short leg is 6 m

The hypotenuse would be 12 m

The longer leg would be 6√3

Perimeter: 6 + 12 + 6√3

The perimeter is 18 + 6√3

Area: 1/2 × b × h

b = 6√3

h = LN = 3√3

6√3 × 3√3

18√9 = 18 × 3 = 54

Area: 54 m²

Hope it helps!!