the perimeter of right angle triangle is 60 cm and its area is 120 CM square find the length of its sides
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Answers
Answer:
hi
Step-by-step explanation:
answer is 10cm ,24 cm ,and 26 cm
Answer:
24cm , 26cm , 10cm
Step-by-step explanation:
Let the sides of a right angled triangle be
a cm , b cm and c cm
Let c cm be the hypotenuse
Perimeter of a right angled triangle = ( a+b+c ) cm
According to the given problem
Perimeter of the given right angled triangle
= 60 cm
=> a+b+c = 60 ------------------(1)
=> c = 60-(a+b) ------------------(2)
and
Area of a right angled triangle
= (1/2) ab sq.cm
According to the given problem
Area of the right angled triangle = 120 cm
=> (1/2) ab = 120
=> ab = 120×2
=> ab = 240 ------------------------(3)
We know that
By Pythagoras Theorem ,
c² = a²+b² --------------------------(4)
On substituting the value of c from (2) in (4)
=> [60-(a+b)]² = a²+b²
=>[60-(a+b)]² = (a+b)² -2ab
=> (60)² -2(60)(a+b)+(a+b)² = (a+b)² -2ab
=> 3600-120(a+b)+(a+b)² = (a+b)²-2(240)
=> 3600-120(a+b)+(a+b)² = (a+b)² -480
=> 3600-120(a+b)+480 = (a+b)²-(a+b)²
=> 4080-120(a+b) = 0
=> 4080 = 120(a+b)
=> (a+b) = 4080/120
=> (a+b) = 408/12
=> (a+b) = 34 --------------------(5)
Substituting this value in (2) then
c = 60-34
=> c = 26 cm
We know that
(a-b)² = (a+b)²-4ab
=> (a-b)² = (34)²-4(240)
=> (a-b)² = 1156-960
=> (a-b)² = 196
=> a-b = ±√196
=> a-b = ±14
The lengths of the sides can't be negative .
a-b = 14 -----------------------------(6)
On adding (5) and (6)
a + b = 34
a - b = 14
(+)
_________
2a + 0 = 48
_________
=> 2a = 48
=> a = 48/2
=> a = 24 cm
From (5)
=> 24+b = 34
=> b = 34-24
=> b = 10 cm
Therefore, a = 24 cm
a = 24 cm b = 10 cm
a = 24 cm b = 10 cmc = 26 cm
The three sides of the triangle are 24 cm, 10 cm and 26 cm