Question

Construct a triangle ABC in
which angle A =45,angle B=90* and its perimeter is14 cm

Answer 1

Answer:

angles : A = 45°, B = 90°, C = 45°

sides : a=4.1cm, b = 5.8cm, c =4.1cm

Step-by-step explanation:

Since Angle A = 45 , angle B = 90 ,

sum of all angles of a Triangle = 180

hence, angle C = 180 - (90+45) = 45

therefore, its a right angled isosceles triangle

hence a = c (X)

also given that a + b + c = 14 (Y)

and since it is a right angled triangle, acc. to pythagoras theorem

a² + c² = b² (Z)

solving the equations in c and b

=> ( 2c² =b² ) and (2c + b = 14)

=> c.(2 +√2) = 14

=> c = 4.1 , a = 4.1 , b = 5.8

Answer 2

$\huge\boxed{\texttt{\fcolorbox{Red}{aqua}{Hey Mate!!}}}$
$<b><i><font face=Copper black size=4 color=blue>$
Here is your answer.

In Triangle
/_A = 45°
/_B = 90°
Hence /_C = 180° - 90° - 45° = 45°

If two angle are same then their side opposite are same Let Side be x cm
Let Hypotenuse is y cm
So By using Pythagoras Theorem
${y}^{2} = {x}^{2} + {x}^{2} \\ {y}^{2} = 2 {x}^{2} \\ y = \sqrt{2} x$
Perimeter of Triangle is 14 cm
$x + x + y = 14 \\ 2x + y = 14 \\ 2x + \sqrt{2} x = 14 \\ x(2 + 1.41) = 14 \\ 3.41x = 14 \\ x = \frac{14}{3.41} \\ x = 4.10$
Now y = √2× 4.10
= 1.41 × 4.10
=5.78 cm

Therefore we Construct a triangle whose sides are 4.10cm , 4.10cm and 5.78 cm


$\large{\red{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\boxed{\underline{\underline{\underline{Hope \: it \: helps\: you}}}}}}}}}}}}}}}$

$\huge\boxed{\texttt{\fcolorbox{Red}{yellow}{Be brainly!!}}}$

$<marquee>$
$\huge\bf{\huge{\bf{\bf{@...rajeev378}}}}$