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NikAS [45]
3 years ago
14

What is the perimeter of the figure​

Mathematics
1 answer:
Natalija [7]3 years ago
7 0

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

\sin 45 = \frac{\textrm{side opposite to angle 45}}{Hypotenuse}\\

we Know sin 45 = 1/√2

∴ \frac{1}{\sqrt{2} }= \frac{LT}{18\sqrt{2}}\\\\\therefore LT = 18\ unit\\\\\therefore TS = 18\ unit\\

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

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