Math / Geometry

QuestionUsing Pythagoras' theorem, calculate the length of PR. Give your answer in centimetres (cm) and give any decimal answers to 1 d .p.
Not drawn accurately

Studdy Solution

STEP 1

1. The triangle is a right triangle with PR as one of the legs, RQ as the other leg, and PQ as the hypotenuse.
2. We will use Pythagoras' theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

STEP 2

1. Identify the known values and the unknown value.
2. Apply Pythagoras' theorem to solve for the unknown side.
3. Calculate the length of PR and round to 1 decimal place.

STEP 3

Identify the known values: - RQ = 28 cm - PQ = 35 cm (hypotenuse) - PR = ? (unknown side)

STEP 4

Apply Pythagoras' theorem: $PQ^2 = PR^2 + RQ^2$
Substitute the known values into the equation: $35^2 = PR^2 + 28^2$

STEP 5

Calculate the squares of the known values: $35^2 = 1225$ $28^2 = 784$
Substitute these values back into the equation: $1225 = PR^2 + 784$

STEP 6

Solve for $PR^2$ by isolating it on one side of the equation: $PR^2 = 1225 - 784$ $PR^2 = 441$

STEP 7

Calculate the length of PR by taking the square root of $PR^2$ : $PR = \sqrt{441}$ $PR = 21$
Since the result is a whole number, no rounding is needed.
The length of PR is:
$\boxed{21 \text{ cm}}$

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QuestionUsing Pythagoras' theorem, calculate the length of PR. Give your answer in centimetres (cm) and give any decimal answers to 1 d .p.
Not drawn accurately

Studdy Solution

STEP 1

STEP 2

1. Identify the known values and the unknown value.
2. Apply Pythagoras' theorem to solve for the unknown side.
3. Calculate the length of PR and round to 1 decimal place.

STEP 3

Identify the known values: - RQ = 28 cm - PQ = 35 cm (hypotenuse) - PR = ? (unknown side)

STEP 4

Apply Pythagoras' theorem: $PQ^2 = PR^2 + RQ^2$
Substitute the known values into the equation: $35^2 = PR^2 + 28^2$

STEP 5

Calculate the squares of the known values: $35^2 = 1225$ $28^2 = 784$
Substitute these values back into the equation: $1225 = PR^2 + 784$

STEP 6

Solve for $PR^2$ by isolating it on one side of the equation: $PR^2 = 1225 - 784$ $PR^2 = 441$

STEP 7

Calculate the length of PR by taking the square root of $PR^2$ : $PR = \sqrt{441}$ $PR = 21$
Since the result is a whole number, no rounding is needed.
The length of PR is:
$\boxed{21 \text{ cm}}$

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QuestionUsing Pythagoras' theorem, calculate the length of PR. Give your answer in centimetres (cm) and give any decimal answers to 1 d .p.Not drawn accurately

Studdy Solution

STEP 1

STEP 2

1. Identify the known values and the unknown value.2. Apply Pythagoras' theorem to solve for the unknown side.3. Calculate the length of PR and round to 1 decimal place.

STEP 3

Identify the known values: - RQ = 28 cm - PQ = 35 cm (hypotenuse) - PR = ? (unknown side)

STEP 4

Apply Pythagoras' theorem: PQ2=PR2+RQ2 PQ^2 = PR^2 + RQ^2 PQ2=PR2+RQ2Substitute the known values into the equation: 352=PR2+282 35^2 = PR^2 + 28^2 352=PR2+282

STEP 5

Calculate the squares of the known values: 352=1225 35^2 = 1225 352=1225 282=784 28^2 = 784 282=784Substitute these values back into the equation: 1225=PR2+784 1225 = PR^2 + 784 1225=PR2+784

STEP 6

Solve for PR2 PR^2 PR2 by isolating it on one side of the equation: PR2=1225−784 PR^2 = 1225 - 784 PR2=1225−784 PR2=441 PR^2 = 441 PR2=441

STEP 7

Calculate the length of PR by taking the square root of PR2 PR^2 PR2: PR=441 PR = \sqrt{441} PR=441​ PR=21 PR = 21 PR=21Since the result is a whole number, no rounding is needed. The length of PR is:21 cm \boxed{21 \text{ cm}} 21 cm​

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QuestionUsing Pythagoras' theorem, calculate the length of PR. Give your answer in centimetres (cm) and give any decimal answers to 1 d .p.
Not drawn accurately

1. Identify the known values and the unknown value.
2. Apply Pythagoras' theorem to solve for the unknown side.
3. Calculate the length of PR and round to 1 decimal place.

Apply Pythagoras' theorem: $PQ^2 = PR^2 + RQ^2$
Substitute the known values into the equation: $35^2 = PR^2 + 28^2$

Calculate the squares of the known values: $35^2 = 1225$ $28^2 = 784$
Substitute these values back into the equation: $1225 = PR^2 + 784$

Solve for $PR^2$ by isolating it on one side of the equation: $PR^2 = 1225 - 784$ $PR^2 = 441$

Calculate the length of PR by taking the square root of $PR^2$ : $PR = \sqrt{441}$ $PR = 21$
Since the result is a whole number, no rounding is needed.
The length of PR is:
$\boxed{21 \text{ cm}}$