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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1053
GPA: 3.39
A small, rectangular park has a perimeter of 560 feet and a diagonal m
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08 May 2022, 08:28
08 May 2022, 08:28
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A small, rectangular park has a perimeter of 560 feet and a diagonal measurement of 200 feet. What is its area, in square feet?
A. 19,200
B. 19,600
C. 20,000
D. 20,400
E. 20,800
A. 19,200
B. 19,600
C. 20,000
D. 20,400
E. 20,800
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: A small, rectangular park has a perimeter of 560 feet and a diagonal m
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08 May 2022, 08:40
08 May 2022, 08:40
2
GeminiHeat wrote:
A small, rectangular park has a perimeter of 560 feet and a diagonal measurement of 200 feet. What is its area, in square feet?
A. 19,200
B. 19,600
C. 20,000
D. 20,400
E. 20,800
A. 19,200
B. 19,600
C. 20,000
D. 20,400
E. 20,800
Let L and W equal the length and width of the rectangle respectively.
perimeter = 560
So, L + L + W + W = 560
Simplify: 2L + 2W = 560
Divide both sides by 2 to get: L + W = 280
diagonal = 200
The diagonal divides the rectangle into two RIGHT TRIANGLES.
Since we have right triangles, we can apply the Pythagorean Theorem.
We get L² + W² = 200²
NOTE: Our goal is to find the value of LW [since this equals the AREA of the rectangle]
If we take L + W = 280 and square both sides we get (L + W)² = 280²
If we expand this, we get: L² + 2LW + W² = 280²
Notice that we have L² + W² "hiding" in this expression.
That is, we get: L² + 2LW + W² = 280²
We already know that L² + W² = 200², so, we'll take L² + 2LW + W² = 280² and replace L² + W² with 200² to get:
2LW + 200² = 280²
So, 2LW = 280² - 200²
Evaluate: 2LW = 38,400
Solve: LW = 19,200
Answer: A
Cheers,
Brent
A small, rectangular park has a perimeter of 560 feet and a diagonal m
[#permalink]
08 May 2022, 09:46
08 May 2022, 09:46
1
Perimeter of rect = 2(L+W) = 560 ----> (L+W) = 280 -----> (L+W)^2 = 280^2 -----> L^2 + W^2 + 2LW = 280^2 ------> L^2 + W^2 = 200^2 (using Pythagoras theorem) ----> 200^2 + 2LW = 280^2
2LW = 280^2 - 200^2
2LW = (280+200)*(280-200)
LW = (480 * 80)/2
LW = 19,200
Hence area of rectangle is equal to 19,200 and correct ans is option A
2LW = 280^2 - 200^2
2LW = (280+200)*(280-200)
LW = (480 * 80)/2
LW = 19,200
Hence area of rectangle is equal to 19,200 and correct ans is option A
