Question

A triangular swimming area is marked off by a rope.

a. If a woman swims around the perimeter of the swimming area, how far will she swim?
b. What is the area of the roped off section?

Answer 1

#a

Perimeter=Sum of sides

• 400+200√6+200+200√3
• 600+200(√6+√3)
• 600+200(2.6+1.7)
• 600+200(4.3)
• 600+860
• 1460m

#b

Area:-

• 1/2×Base×Height
• 1/2(200+200√3)(200√3)
• (200+200(1.7))100√3
• (200+340)(170)
• 540(170)
• 91800m²

Answer 2

Perimeter = 1436.3 m (nearest tenth)

Area = 94641.0 m² (nearest tenth)

Explanation:

The perimeter is the sum of the lengths of all the sides.

`\begin{aligned}\sf \implies perimeter & =400+200√(6)+200√(3)+200\\ & =1436.30811\\ & = 1436.3 \: \sf m\:(nearest\:tenth)\end{aligned}`

`\begin{aligned}\textsf{Area of a triangle} & =\sf \frac12 * base \ height\\ & = \sf \frac12 * (200+200√(3)) * 200√(3)\\ & =94641.01615\\ & = 94641.0\: \sf m^2\:(nearest\:tenth)\end{aligned}`