in a triangle , angle b=90°, ab=2x+1 cm& bc=x+1cm. if area of a triangle is 60 cm2 , find perimeter
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in triangle abc
ab is the height and bc is the base
so,
area=1/2*base*height
so,
60=1/2*(x+1)*(2x+1)
120=2x^2+3x+1
2x^2+3x=120-1
2x^2+3x-119=0
2x^2+17x-14x-119=0
x(2x+17)-14(2x+17)
(x-14)(2x+17)
so,x=14 or x=-17/2
since x cannot be a negative no. we take x as 14
so,
ab=29 cm and bc=15 cm
so,ac^2=ab^2+bc^2
ac^2=841+225
ac=32.64 cm
so perimeter=32.64+15+29=76.64 cm
ab is the height and bc is the base
so,
area=1/2*base*height
so,
60=1/2*(x+1)*(2x+1)
120=2x^2+3x+1
2x^2+3x=120-1
2x^2+3x-119=0
2x^2+17x-14x-119=0
x(2x+17)-14(2x+17)
(x-14)(2x+17)
so,x=14 or x=-17/2
since x cannot be a negative no. we take x as 14
so,
ab=29 cm and bc=15 cm
so,ac^2=ab^2+bc^2
ac^2=841+225
ac=32.64 cm
so perimeter=32.64+15+29=76.64 cm
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