Question

The perimeter of a right angled triangle is 144 cm and the hypotenuse is 65 cm. Its
area is square cm is ....

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Answer 1

Answer:

First of all we create a system of equations:

x and y are the legs of a triangle

x²+y²=65² and x+y+65=144

x²+y²=65² and x+y=79 → x=79–y

(79–y)²+y²=65²

79²–2×79y+y²+y²=65²

2y²–158y+79²–65²=0

2y²–158y+(79+65)×(79–65)

2y²–158y+144×14

2y²–158y+2016=0

y²–79y+1008=0