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Hypoteneous of a right angle triangle is 2 meter square than perpendicular and base is also 1 metar longer than perpendicular . find the length of hypoteneous. |
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Answer» -STEP explanation:Since the hypotenuse of a right triangle is 2 cm more than the longer side of the triangle and the shorter side of the triangle is 7 cm less than the longer side,therefore, the hypotenuse =x+9, ONE side =x and the other side =x+7.From here, you apply Pythagorean theorem:a 2 +b 2 =C 2 wherec is length of hypotenusea and b are the LENGTHS of the two sides.x 2 +(x+7) 2 =(x+9) 2 x 2 +(x+7)(x+7)=(x+9)(x+9)x 2 +(x 2 +14x+49)=(x 2 +18x+81)2x 2 +14x+49=x 2 +18x+81x 2 −4x−32=0Factoring:(x−8)(x+4)=0x=−4,8We can THROW out the negative solution leaving:x=8 cm (short legth)long legth =x+7=8+7=15 cmhypotenuse =x+9=8+9=17 cm Hence, the length of the hypotenuse is 17 cm. |
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