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.
Answers
Answered by
5
Step-by-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
where
c is length of hypotenuse
a 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+81
x
2
−4x−32=0
Factoring:
(x−8)(x+4)=0
x=−4,8
We can throw out the negative solution leaving:
x=8 cm (short legth)
long legth =x+7=8+7=15 cm
hypotenuse =x+9=8+9=17 cm
Hence, the length of the hypotenuse is 17 cm.
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0
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