Junior Cycle Mathematics Geometry: Cillian is making a ramp for a d

Cillian is making a ramp for a different building - Junior Cycle Mathematics - Question (b) - 2016

Question (b)

Cillian is making a ramp for a different building. His ramp is also in the shape of a right-angled triangle. A diagram of his ramp is shown below. Use the Theorem of... show full transcript

Worked Solution & Example Answer:Cillian is making a ramp for a different building - Junior Cycle Mathematics - Question (b) - 2016

Step 1

Use the Theorem of Pythagoras

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Answer

The Theorem of Pythagoras 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. We can express this mathematically as:

$x^2 + 224^2 = 226^2$

where:

$x$ = length of the ramp
$224 ext{ cm}$ = one side of the triangle
$226 ext{ cm}$ = the hypotenuse.

Step 2

Calculate $224^2$ and $226^2$

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Answer

Calculating the squares:

$224^2 = 50176$ $226^2 = 51076$

Step 3

Substitute the squared values back into the equation

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Answer

We substitute back into the equation:

$x^2 + 50176 = 51076$

Step 4

Isolate $x^2$

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Answer

Next, we isolate $x^2$ by subtracting $50176$ from both sides:

$x^2 = 51076 - 50176$ $x^2 = 900$

Step 5

Find $x$

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Answer

Finally, we take the square root of both sides to find $x$ :

$x = \\sqrt{900} = 30 ext{ cm}$

Cillian is making a ramp for a different building - Junior Cycle Mathematics - Question (b) - 2016

Worked Solution & Example Answer:Cillian is making a ramp for a different building - Junior Cycle Mathematics - Question (b) - 2016

Use the Theorem of Pythagoras

Calculate $224^2$ and $226^2$

Substitute the squared values back into the equation

Isolate $x^2$

Find $x$

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