Any triangle with one angle equal to 90⁰ produces a Pythagoras triangle and the Pythagoras equation can be applied in the triangle.
<h3>What is the Pythagoras Theorem?</h3>
The Pythagoras theorem states that if a triangle is right-angled (90 degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In △ABD and △ACB,
∠A = ∠A (common)
∠ADB = ∠ABC (both are right angles)
Thus, △ABD ∼ △ACB (by AA similarity criterion)
Similarly, we can prove △BCD ∼ △ACB.
Thus △ABD ∼ △ACB,
Therefore, AD/AB = AB/AC.
We can say that AD × AC = AB².
Similarly, △BCD ∼ △ACB.
Therefore,
CD/BC = BC/AC.
We can also say that
CD × AC = BC².
Adding these 2 equations, we get
AB² + BC² = (AD × AC) + (CD × AC)
AB² + BC² =AC(AD +DC)
AB² + BC² = AC²
Hence proved
Thus, any triangle with one angle equal to 90⁰ produces a Pythagoras triangle and the Pythagoras equation can be applied in the triangle.
Learn more about Pythagoras theorem from:
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Well, we know 1 yard is 3 feet, so 2 yards is 6 feet. That makes Jorge's sleeping bag longer than Jim's. (6 feet is longer than 5 feet)
We also know that 1 yard is 36 inches, so 2 yards is 72 inches. That makes Jorge's sleeping bag longer than Steven's. (72 inches is longer than 68 inches)
Since Jorge's sleeping bag is longer than both Jim's and Steven's, Jorge's sleeping bag is longer.
Answer:
x=11.2
Step-by-step explanation:
