Correct Question : In the diagram, the radius of the outer circle is 2x cm and the radius of the inside circle is 6 cm. The area of the shaded region is 220π cm2. What is the value of x? Enter your answer in the box.

We have ,

the area of a circle = πr²

the outer circle area = $\pi(2x)^2 =4\pi x^2$

the inside circle area = $\pi (6)^2= 36\pi$

According to Question,

the outer circle area - the inside circle area = he shaded region

⇒ $\pi (4x^2)-36\pi =220\pi$

⇒ $x^2-9 =55$

⇒ $x^2=64$

⇒ $x =\sqrt{64}=8$

Therefore , the value of x is 8 cm.

5 0

3 years ago

Triangle JKL is dilated from the origin at a scale factor of 10 to create triangle J′K′L′.Select the option that completes the s

Aneli [31]

Given: Triangle JKL is dilated from the origin at a scale factor of 10 to create triangle J′K′L′.

Required: Correct option that complete the statement.

Explanation:

Now, triangle is dilated from the origin at a scale factor of 10.

So, the sides will become larger, but angles will remain the same.

Hence, the triangles will be similar as sides will be in proption (SSS rule).

So, The triangles are similar because their corresponding sides are proptional and their corresponding angles are congurent.

Final Answer: Second group is correct answer.

5 0

1 year ago