Answer:
The perimeter of the figure is 111.46 units
Step-by-step explanation:
Given:
RS = 43
LS = 18√2
A right Triangle is attached to a Rectangle.
A right Triangle is having measure angle 45° , 90°
and Hypotenuse = 18√2
∴ The Third Angle measure will also be 45° {angles Sum property of a triangle}
∴ the right angled triangle is an Isosceles triangle.
∴ Two sides are equal LT = TS
To Find:
Perimeter of figure = ?
Solution:
we have
[tex]\sin 45 = \frac{\textrm{side opposite to angle 45}}{Hypotenuse}\\[/tex]
we Know sin 45 = 1/√2
∴ [tex]\frac{1}{\sqrt{2} }= \frac{LT}{18\sqrt{2}}\\\\\therefore LT = 18\ unit\\\\\therefore TS = 18\ unit\\[/tex]
Now ,
ARTL is a Rectangle
∴ opposite side of a rectangle are equal
∴ LT = AR = 18 unit
and AL = RT
But,
RT = RS - TS
= 43 - 18
25
∴ AL = RT = 25
∴ Perimeter of figure = AL + LS + RS + AR
= 25 + 18√2 + 43 + 18
= 86 + 18√2
= 111.455
= 111.46 units
∴ Perimeter of figure = 111.46 units
