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THE HYPOTNUSE OF A TRIANGLE IS 1 UNIT MORE THAN 2 TIMES THE BASE.THE HEIGHT IS 7 UNIT MORE THAN THE BASE.FIND THE SIDES OF THE TRIANGLE. |
| Let x be the length of base. Given, Hypotenuse=1+2x Height=x+7 We know, Hypotenuse2=Base2+Altitude2 (1+2x)2=x2+(x+7)2 4x2+4x+1=x2+x2+14x+49 4x2+4x+1=2x2+14x+49 4x2-2x2+4x-14x+1-49=0 2x2-10x-48=0 Dividing by 2, x2-5x-24=0 By factorization, (x-8)(x+3)=0 x=8 or x=-3 Since x is base,it cant be negative. So,x=8 is taken Base=8 Altitude=x+7=8+7=15 Hypotenuse=1+2x=1+2*8=17 |
