the perimeter of a right angled triangle is 144 cm and its hypotenuse is 65 cm find the length of other sides and calculates its area .
Answers
Answer:
length of othersides 63 and 16 cm
area is 604 cm
Step-by-step explanation:
The perimeter of right angled triangle is 144 cm.
hypotenuous is 65 cm .
let the two sides are x and y .
x^2 + y^2 = 652
perimeter of right angled triangle is 144 cm.
And x + y + 65 = 144
x + y = 144 - 65 = 79
squaring both sides, we get
( x + y )^2 = 792
=> x^2 + y^2 + 2 x y = 6241
4225 + 2 x y = 6241
2 x y = 6241 - 4225
= 2016
x y = 2016 / 2
= 1008
y = 1008 / x
substituting
y = 1008 / x in
x + y = 79 , we get
x + 1008 / x = 79
x^2 + 1008 = 79 x
x2 - 79 x +1008 = 0
x2 - 63 x - 16 x + 1008 = 0
x ( x - 63 ) - 16 ( x - 63 ) =0
( x - 63 ) ( x - 16 ) = 0
so, x = 63 cm or x = 16 cm
the length of other sides are 63 cm , 16 cm.
Area of right angled tringle is
1 / 2 x 63 x 16 = 504 cm2
Verify the result using Heron's Formula
S = ( 16 + 63 + 65 ) / 2 = 72
A = ( s x ( s-a ) x ( s - b ) x ( s - c ) )1/2
= ( 72 x (72 - 16 ) x ( 72 - 63 ) x ( 72 - 65 ) )1/2
= ( 72 x 56 x 9 x 7 ) 1/2
= ( 9 x 8 x 8 x 7 x 9 x 7 )1/2
= 9 x 8 x 7 = 504 cm^2