The perimeter of the rectangle is 21.6 m
Further explanation
To solve the above questions, we need to recall some of the formulas as follows:
Area of Square = (Length of Side)²
Perimeter of Square = 4 × (Length of Side)
Area of Rectangle = Length × Width
Perimeter of Rectangle = 2 × ( Length + Width )
Area of Rhombus = ½ × ( Diagonal₁ + Diagonal₂ )
Perimeter of Rhombus = 4 × ( Length of Side )
Area of Kite = ½ × ( Diagonal₁ + Diagonal₂ )
Perimeter of Kite = 2 × ( Length of Side₁ + Length of Side₂ )
Let us now tackle the problem !
Given:
Length of Diagonal = d = 8 m
Angle Between Diagonal and Width = θ = 60°
Unknown:
Perimeter = ?
Solution:
See the picture in the attachment ,
[tex]\sin \theta = \frac{BC}{AC}[/tex]
[tex]\sin 60^o = \frac{BC}{8}[/tex]
[tex]\frac{1}{2} \sqrt{3} = \frac{BC}{8}[/tex]
[tex]BC = 8 \times \frac{1}{2} \sqrt{3}[/tex]
[tex]BC = 4 \sqrt{3}[/tex]
[tex]BC = 4(1.7)[/tex]
[tex]\boxed {BC = 6.8 ~ m}[/tex]
[tex]\cos \theta = \frac{AB}{AC}[/tex]
[tex]\cos 60^o = \frac{AB}{8}[/tex]
[tex]\frac{1}{2} = \frac{AB}{8}[/tex]
[tex]AB = 8 \times \frac{1}{2}[/tex]
[tex]\boxed {AB = 4 ~ m}[/tex]
[tex]Perimeter ~ = 2 ( AB + BC )[/tex]
[tex]Perimeter ~ = 2 ( 4 + 6.8 )[/tex]
[tex]Perimeter ~ = 2 ( 10.8 )[/tex]
[tex]\large {\boxed {Perimeter ~ = 21.6 ~ m} }[/tex]
Learn more
- The perimeter of a polygon : https://brainly.com/question/6361596
- The perimeter of a rectangle : https://brainly.com/question/7619923
- The perimeter of a triangle : https://brainly.com/question/2299951
Answer details
Grade: College
Subject: Mathematics
Chapter: Two Dimensional Figures
Keywords: Perimeter, Area , Square , Rectangle , Side , Length , Width
