Find the lengths of the sides of a right triangle if the hypotenuse 10 centimeters longer than the shorter leg and 5 centimeters longer than the longer leg.

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Rosemary McBride · Accepted Answer

Formula used:  a) In a right triangle square hypotenuse is equal to the sum of the squares of the other two sides.  If hypotenuse is z, longer side is y and smaller side be x, then z2=x2+y2  b) Factorization method of a quadratic polynomial.  The general quadric equation is   ax2+bx+c=0; a, b, c∈Real numbers and a≠0  In quadratic factorization using splitting of middle term which is x term is the sum of the two factors and product is equal to last term.  Step 2  Let the smaller leg be x.  Longer leg by y.  Hypotenuse be z.  According to the problem, hypotenuse is 10 cm longer than the smaller leg.  Therefore,   1) z=10+x  And hypotenuse is 5 cm is longer than the shorter leg.  Therefore,   2) z=5+y  From (1) and (2),  10+x=5+y  ⇒y=10−5+x  ⇒y=5+x  Step 3  We know that, in aright angled triangle, z2=x2+y2  (x+10)2=x2+(x+5)2  ⇒x2+20x+100=x2+x2+10x+25  ⇒x2+20x+100=2x2+10x+25  ⇒2x2−x2+10x−20x+25−100=0  ⇒x2−10x−75=0  ⇒x2−15x+5x−75=0  ⇒x(x−15)+5(x−15)=0  ⇒(x−15)+(x+5)=0  ⇒(x−15)=0 or (x+5)=  ⇒x=15 or x=−15  Length is always positive, therefore x=15  Therefore, smaller ≤g(x)=15 centimeters.  Hypotenuse (z)=10+15=25 centimeters.  Longer ≤(y)=z−5=25−5=20 centimeters.  Step 4  For a give right triangle,  Smaller ≤g=15 centimeters.  Longer ≤g=20 centimeters.  Hypotenuse =25 centimeters.

Find the lengths of the sides of a right triangle if the hypotenuse 10

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