One leg of a right triangle has a length of 7m. The other sides have lengths that are consecutive integers. Find these lengths.
1 answer:
Answer:
24m and 25m.
Step-by-step explanation:
By Pythagoras Theorem:
h^2 = x^2 + 7 ^2 where h is the hypotenuse and x is the other leg.
But x and h are consecutive integers
so h = x + 1 and:
(x + 1)^2 = x^2 + 49
x^2 + 2x + 1 - x^2 = 49
2x + 1 = 49
2x = 48
x = 24
So the 2 lengths are 24 and 25.
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Answer:
45
Step-by-step explanation:
<span>In a triangle the sum of two sides is always greater than the third side.
9-9 < x < 9+9
0 < x < 18 </span>← answer
Let us use the formula with the point (4,5) and (0,2)
![\begin{gathered} d=\sqrt[]{(x_1-x_2)^2+(y_1-y_2)^2}=\sqrt[]{(4-0)^2+(5-2)^2} \\ =\sqrt[]{16+9}=\sqrt[]{25}=5 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20d%3D%5Csqrt%5B%5D%7B%28x_1-x_2%29%5E2%2B%28y_1-y_2%29%5E2%7D%3D%5Csqrt%5B%5D%7B%284-0%29%5E2%2B%285-2%29%5E2%7D%20%5C%5C%20%3D%5Csqrt%5B%5D%7B16%2B9%7D%3D%5Csqrt%5B%5D%7B25%7D%3D5%20%5Cend%7Bgathered%7D)
