Question

Please help with Question 12 at the top, i dont really want the answer. I just want how to figure it out please!

Answer 1

a:
`x = (9√(5))/(5)`.

b:
`x = √(5)`.

c:
`x = (√(10))/(2)`.

Explanation:

Apply the Pythagorean Theorem. The square of the hypotenuse of a right triangle is the sum of the squares of the two legs.

For triangle in a:

• Hypotenuse: 9.
• First Leg: x.
• Second Leg: 2x.

Apply the Pythagorean Theorem.

`9^2 = x^2 + (2x)^2\\9^2 = x^2 + 4 x^2 = 5 x^2\\x^2 = (9^2)/(5)\\x = \sqrt{(9^2)/(5)}\\\phantom{x} = (9)/(√(5))\\\phantom{x} = (9√(5))/(5)`
.

As a result,
`x = (9√(5))/(5)`.

Try the same steps for the triangle in b.
`x = √(5)`.

Question c includes a rectangle. The lengths of opposite sides of a rectangle are equal. As a result, for the right triangle with a right angle at the lower-right corner of the rectangle:

• Hypotenuse: 5.
• First Leg: x.
• Second Leg: 2x.

Apply the Pythagorean Theorem:

`5^2 = x^2 + (3x)^2\\25 = x^2 + 9x^2\\10 x^2 = 25\\x^2 = (5)/(2)\\x = \sqrt{(5)/(2)}\\\phantom{x} = (√(5 * 2))/(2)\\\phantom{x} = (√(10))/(2)`

As a result,
`x = (√(10))/(2)`