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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?
hi,...this question also just need to picturise the triangle...
Let a and b be the two sides of the triangle such that a is longer than b. The statement "the hypotenuse of a right triangle is 2 centimeters more than the longer side of the triangle" may be formulated by
h = a + 2 or a = h - 2
The statement "the shorter side of the triangle is 7 centimeters less than the longer side" may be formulated
b = a - 7 or b = (h - 2) - 7 = h - 9
We now use Pythagoras’s theorem to write a third equation
h 2 = a 2 + b 2
Substitute a by h - 2 and b by h - 9 in the above equation to obtain an equation in one variable only:
h 2 = (h - 2) 2 + (h - 9) 2
Simplify and rewrite the above equation in standard form.
h 2 -22 h + 85 = 0
Solve for h.
h = 5 and h = 17.
Only the solution h = 17 gives a and b positive and it is the length of the hypotenuse of the triangle.
17
consider the longer side as x then hyp.=x+2
and shorter side =x-7
now apply hypotneous th.
sovle the quadratic eqn to get the ans 15&3 but 15 is longer so reject 3
hence hyp =15+2=17
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