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AQA GCSE · Question 06 · Geometry and Measures
Here is a right-angled triangle.
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Use Pythagoras' theorem to show that x = 0.8
Here is a right-angled triangle.
<br>
<br>
Use Pythagoras' theorem to show that x = 0.8
How to approach this question
1. Identify the hypotenuse (the longest side, opposite the right angle) and the other two sides (the legs).
2. Write down Pythagoras' theorem: a² + b² = c², where c is the hypotenuse.
3. Substitute the given values into the theorem.
4. Rearrange the equation to make x² the subject.
5. Calculate the values and solve for x.
Full Answer
Pythagoras' theorem states that for a right-angled triangle with legs a and b and hypotenuse c, a² + b² = c².
In this triangle:
The two shorter sides (legs) are x cm and 1.5 cm.
The longest side (hypotenuse) is 1.7 cm.
So, we can write the equation:
x² + 1.5² = 1.7²
Now, calculate the squares:
1.5² = 2.25
1.7² = 2.89
Substitute these values back into the equation:
x² + 2.25 = 2.89
To find x², subtract 2.25 from both sides:
x² = 2.89 - 2.25
x² = 0.64
To find x, take the square root of both sides:
x = √0.64
x = 0.8
This shows that x = 0.8.
Pythagoras' theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Here, the hypotenuse is 1.7 cm. The other two sides are x cm and 1.5 cm.
According to the theorem:
x² + 1.5² = 1.7²
Calculate the squares:
x² + 2.25 = 2.89
Subtract 2.25 from both sides to isolate x²:
x² = 2.89 - 2.25
x² = 0.64
Take the square root of both sides to find x:
x = √0.64
x = 0.8
Thus, we have shown that x = 0.8.
Common mistakes
✗ Incorrectly identifying the hypotenuse. A common mistake is to always add the two given numbers squared, e.g., 1.5² + 1.7² = x². This is wrong because x is one of the shorter sides.
✗ Calculation errors, especially when squaring decimals without a calculator or inputting them incorrectly.
✗ Forgetting to take the square root at the end.
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