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the length of the hypotenuse of …

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the length of the hypotenuse of a right triangle exceeds the base by 1 cm and also exceeds twice the length of the altitude by 3 cm. Find the length of each side of the triangle
  • 1 answers

Ram Kushwah 6 years, 9 months ago

Let base =x

then hypo=x+1

Let altitude =h

also hypo=2h+3

h=(hypo-3)/2------(1)

=(x+1-3)/2=(x-2)/2

Now Hypo2=h2+x2

(x+1)2=1/4*(x-2)2 +x2

{tex}\begin{array}{l}4(x+1)^2=(x-2)^2+4x^2\\4x^2+8x+4=x^2-4x+4+4x^2\\x^2-12x=0\\x(x-12)=0\\x=0\;or\;12\\\end{array}{/tex}

The side can not be zero 

so x= base =12 cm

Hypo=12+1=13 cm

From(1)

h=(13-3)/2= 5 cm

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