the perimeter of a right angle triangle is 12 cm and its hypotenuse is 5 cm cm find both side and area of the triangle verify the result obtained by heron's formula
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Let the two legs of the triangle be x and y.
Then x+y+5=12 and x2+y2=52
y=7−x
Substituting:
x2+(7−x)2=25
x2+49−14x+x2=25
2x2−14x+24=0
2(x2−7x+12)=0
2(x−3)(x−4)=0
x=3and4
The two legs measure 3 and 4 cm. The area is given by A=B×H2, where B and H are the two legs.
A=3×42
A=6 square centimetres
Then x+y+5=12 and x2+y2=52
y=7−x
Substituting:
x2+(7−x)2=25
x2+49−14x+x2=25
2x2−14x+24=0
2(x2−7x+12)=0
2(x−3)(x−4)=0
x=3and4
The two legs measure 3 and 4 cm. The area is given by A=B×H2, where B and H are the two legs.
A=3×42
A=6 square centimetres
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