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Serggg [28]
3 years ago
12

The hypotenuse of a right triangle is 13cm long. the longer leg is 7 cm longer than the shorter leg. find the side lengths of th

e triangle.
Mathematics
1 answer:
Ad libitum [116K]3 years ago
8 0

5^2 + 12^2 = 13^2


is the second or third Pythagorean triple on the list, which gives us the answer directly.


But if we didn't know that, let x be the short leg:


x^2 + (x+7)^2 = 13^2


2x^2 + 14 x + 49 - 169 = 0


x^2 + 7x  - 60 = 0


(x+12)(x-5)=0


Rejecting the negative root, x=5, other side 12, the Pythagorean triple we found.

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Evaluate the expression when c=4 and d=48. d-6c​
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statuscvo [17]

Answer:

(x-230)^2+(y-220)^2=6100

Step-by-step explanation:

The equation for a circle is (x-h)^2+(y-k)^2=r^2, where (h,k) is the vertex of the circle and r is the radius. Immediately, since the center of the circle is given, we know what h and k are. h is 230 and k is 220.

The only thing we need to find is the radius, which will just be the distance from the center (230,220) to a point on the circumference (170,170). The distance between them can be calculated using the <u>distance formula</u>, which is really just the <u>Pythagorean Theorem</u> rearranged. The formula states that d=\sqrt{x^2+y^2}, where x is the change in the x-coordinates of the two points and y is the change in the y-coordinates of the two points. Plug-in x for 60 and y for 50 to get d=\sqrt{50^2+60^2}. Solve for d, arriving at \sqrt{6100}. Therefore, the radius of the circle is \sqrt{6100}.

Finally, we have all of the components to create the equation of the circle. Plug-in 230 for h, 220 for k, and \sqrt{6100} for r.

The equation of the circle will be (x-230)^2+(y-220)^2=6100.

Hope this helps :)

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2 years ago
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