the length of the hypotenuse of a rigth triangled triangle is 10cm more than the length of the longer of the 2sides. calculate the lengths of the hypotenuse and the other unknow
n side if the length of the shortest side is 50 cm
50^2 + x^2 = (x+10)^2
To solve this problem, let's assign variables to the unknown lengths. Let's call the length of the longer side "x" cm and the length of the hypotenuse "y" cm.
It is given that the length of the shortest side is 50 cm. So, we have the following information:
Shortest side = 50 cm
Longer side = x cm
Hypotenuse = y cm
According to the problem, the length of the hypotenuse is 10 cm more than the length of the longer side. So, we can write an equation for this relationship:
y = x + 10
Now, let's use the Pythagorean theorem to relate the three sides of a right-angled triangle:
(Shortest side)^2 + (Longer side)^2 = (Hypotenuse)^2
Substituting the known values into the equation, we get:
50^2 + x^2 = y^2
We can substitute the value of y from the first equation into the second equation:
50^2 + x^2 = (x + 10)^2
Let's simplify this equation:
2500 + x^2 = x^2 + 20x + 100
Subtracting x^2 from both sides, we get:
2500 = 20x + 100
Subtracting 100 from both sides, we have:
2400 = 20x
Dividing by 20, we get:
x = 120
So, the length of the longer side is 120 cm.
Now, we can substitute this value into the first equation to find the length of the hypotenuse:
y = x + 10
y = 120 + 10
y = 130
Therefore, the length of the hypotenuse is 130 cm.
In summary, the length of the hypotenuse is 130 cm, and the length of the longer side is 120 cm.