To answer this item, we make use of the equation derive from the Pythagorean theorem for right triangles which states that the square of the hypotenuse (the longest side) is equal to the sum of the squares of the two shorter sides. If we let x be the measure of both the shorter sides (we call this as legs), we have,
(14 in)² = (x²) + (x²)
Simplifying the equation,
196 in² = 2x²
Divide both sides of the equation by 2,
98 in² = x²
To get the value of x, we get the square root of both sides of the equation,
x = sqrt (98) = 7√2 inches
Hence, the measure of each leg of the right triangle is 7√2 inches or approximately 9.9 inches.
Speed = distance / time
speed = 135/3 = 45 miles per hr <==
(x-1)^3 / 2 = 27
For equations like this, we want to isolate x in order to get the value of it.
First, let's multiply both sides by 2 to eliminate the fraction.
(x-1)^3 = 27(2)
Now, let's take the cube root of both sides
(x-1) = ∛(27 * 2)
Now, simplify the root
x - 1 = 3∛2
Add both sides by 1
x = 1 + 3∛2
That's your answer.
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