The hypotenuse of a right triangle is 2 centimeters more than the longer side of the triangle. The shorter side of the triangle is 7 centimeters less than the longer side. Find the length of the...
The hypotenuse of a right triangle is 2 centimeters more than the longer side of the triangle.
The shorter side of the triangle is 7 centimeters less than the longer side. Find the length of the hypotenuse.
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calendarEducator since 2010
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Let the three sides of the triangle be a, b and c.
Let the shorter side be a, the longer side be b and the hypotenuse be c.
It is given that the shorter side of the triangle is 7 centimeters less than the longer side.
=> a = b - 7
The hypotenuse of triangle is 2 more than the longer side of the triangle.
=> c = b + 2
Now we use the Pythagorean Theorem
a^2 + b^2 = c^2
=> (b - 7)^2 + b^2 = (b + 2)^2
=> b^2 + 49 - 14b + b^2 = b^2 + 4 + 4b
=> b^2 + 45 - 18b = 0
=> b^2 - 15b - 3b + 45 = 0
=> b(b - 15) - 3(b - 15) = 0
=> (b - 3)(b - 15) = 0
b = 3 and b = 15
b cannot be 3 as b - 7 would be negative
c = b + 2 = 17
The length of the hypotenuse is 17 cm.
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calendarEducator since 2008
write3,662 answers
starTop subjects are Math, Science, and Social Sciences
Let the sides be x, y and the hypotenuse h.
Given that h is 2 more than the longer sides.
Let the longer side be x.
==> h = x+2...............(1)
The shorter side (y) is 7 less than the longer sides.
==> y= x-7 ..............(2)
But we know that L
h^2 = x^2 + y^2
==> (x+2)^2 = x^2 + (x-7)^2
==> x^2 + 4x +4 = x^2 + x^2 -14x + 49
==> x^2 + 4x +4 = 2x^2 -14x + 49
==> x^2 -18x + 45 = 0
==> (x-3)(x-15) = 0
==> x1= 3 ==> y= 3-7 = -4 (impossible)
==> x2=15 ==> y2= 15-7 = 8
==> h= 15+2 = 17
Then, the length of the hypotenuse is 17 cm.