find the perimeter of an isosceles right triangle whose area is 200 cm
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Answer:
Step-by-step explanation:
Find the perimeter of an isosceles right triangle whose area is 200 cm^2.
since , we know that in isosceles triangle two sides are always equal. but here given that the isosceles triangle is right triangle . if the triangle is isosceles right triangle then its base and height will be equal.
why hypotenuse will not be equal either to height or base of isosceles right triangle ?
its because , according pythagoras theorem
if the triangle is right (90°) then the length of hypotenuse of that triangle will always be greater than the base and the height of that triangle.
let b be the hypotenuse and ( a , a ) be the base and height of isosceles right triangle.
from ∆ ABC
area of isosceles right triangle=200cm^2
( 1 / 2 ) × base × height = 200
( 1 × a × a ) / 2 = 200
a^2 = 400 => a = √400 => a = 20 cm
now in ∆ ABC ,
by Pythagoras theorem , we get
(AC)^2 = ( BC )^2 + ( AB )^2
b^2 = ( 20 )^2 + ( 20 )^2
b^2 = 400 + 400 = 800
b = √800 => 28.2 cm ( approx. )
since , we know that perimeter of triangle
= sum of all the sides of triangle.
therefore, perimeter of isosceles right triangle
= a + a + b = 20 + 20 + 28.2 = 68.2 cm
Your Answer : 68.2 cm
THEREFORE, Perimeter of an isosceles right triangle whose area is 200 cm= 68.2 cm