i) Use the diagram on the right to calculate the value of x. Give your answer in surd form. ii) Use the diagram below to calculate the value of y. Give your answer in surd form. iii) A rectangle with sides of length x and y is drawn using the values of x and y from parts (i) and (ii), as shown below. Write the perimeter of this rectangle in the form a√2, where a ∈ N.

Photo AI

i) Use the diagram on the right to calculate the value of x - Junior Cycle Mathematics - Question Question 1 - 2014

Question Question 1

i) Use the diagram on the right to calculate the value of x. Give your answer in surd form. ii) Use the diagram below to calculate the value of y. Giv... show full transcript

Worked Solution & Example Answer:i) Use the diagram on the right to calculate the value of x - Junior Cycle Mathematics - Question Question 1 - 2014

Step 1

Use the diagram on the right to calculate the value of x.

96%

114 rated

Answer

To find the value of x in the right triangle, we can use the Pythagorean theorem.

The sides of the triangle are 3 (adjacent) and 3 (opposite), thus:

$x^2 = 3^2 + 3^2$ $x^2 = 9 + 9$ $x^2 = 18$ $x = rac{3}{ ext{sqrt}(2)} = 3 ext{sqrt}(2)$

Hence, the value of x is $3 ext{sqrt}(2)$ .

Step 2

Use the diagram below to calculate the value of y.

99%

104 rated

Answer

In the second triangle, the sides are 1 (adjacent) and 3 (opposite).

Again using the Pythagorean theorem:

$y^2 = 1^2 + 3^2$ $y^2 = 1 + 9$ $y^2 = 10$ $y = ext{sqrt}(10)$

Therefore, the value of y is $ext{sqrt}(10)$ .

Step 3

Write the perimeter of this rectangle in the form a√2, where a ∈ N.

96%

101 rated

Answer

The perimeter P of a rectangle is calculated using the formula:

$P = 2x + 2y$

Substituting the values of x and y from parts (i) and (ii):

$P = 2(3 ext{sqrt}(2)) + 2( ext{sqrt}(10))$ $P = 6 ext{sqrt}(2) + 2 ext{sqrt}(10)$

Thus, the perimeter can be expressed as $10$ .

Join the Junior Cycle students using SimpleStudy...

97% of Students

Report Improved Results

98% of Students

Recommend to friends

100,000+

Students Supported

1 Million+

Questions answered

;