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555-605 (Medium)|   Geometry|      
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Bunuel
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In the figure shown, J, K, and L are the centers of the three circles. 13 Oct 2020, 03:00
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74% (02:50) correct 26% (03:28) wrong based on 61 sessions

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In the figure shown, J, K, and L are the centers of the three circles. The radius of the circle with center J is four times the radius of the circle with center L, and the radius of the circle with center J is two times the radius of the circle with center K. If the sum of the areas of the three circles is 525π square units, what is the measure, in units, of JL?

A. 35

B. 45

C. 50

D. 65

E. 70


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In the figure shown, J, K, and L are the centers of the three circles. 13 Oct 2020, 05:15
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Bunuel, What is the sum of the areas of the 3 circles? It's not clear in the question.
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In the figure shown, J, K, and L are the centers of the three circles. 13 Oct 2020, 05:23
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Bunuel, What is the sum of the areas of the 3 circles? It's not clear in the question.
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Fixed. Thank you!
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In the figure shown, J, K, and L are the centers of the three circles. 13 Oct 2020, 10:50
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Bunuel

In the figure shown, J, K, and L are the centers of the three circles. The radius of the circle with center J is four times the radius of the circle with center L, and the radius of the circle with center J is two times the radius of the circle with center K. If the sum of the areas of the three circles is 525π square units, what is the measure, in units, of JL?

A. 35

B. 45

C. 50

D. 65

E. 70
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Use x for the radius of the small circle. Then the medium circle has radius 2x and the large circle has radius 4x. Calculate their areas.

→ Small circle: A = πx²

→ Medium circle: A = π(2x)² = 4πx²

→ Large circle: A = π(4x)² = 16πx²

The total area is 21πx². Set this equal to 525π and solve for x.

→ 21πx² = 525π

→ x² = 25

→ x = 5

Therefore, the radii of the three circle are 5, 10, and 20. Calculate the answer.

→ JL = 20 + 10 + 10 + 5 = 45
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In the figure shown, J, K, and L are the centers of the three circles. 13 Oct 2020, 12:57
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In the figure shown, J, K, and L are the centers of the three circles. The radius of the circle with center J is four times the radius of the circle with center L, and the radius of the circle with center J is two times the radius of the circle with center K. If the sum of the areas of the three circles is 525π square units, what is the measure, in units, of JL?

Let's radius of L = x, so for K = 2x & for J = 4x
Area of L = π x^2, for K = 4 π x^2, for J = 16 π x^2

Total Area 21 π x^2 = 525 π, so x = 5

Now JL = 4x + 2x + 2x + x
= 9x = 9x5 = 45

Ans: B
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