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Perimeter of a small rectangular park is 560 feet and measure of its
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05 Jan 2025, 14:06
05 Jan 2025, 14:06
Expert Reply
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Question Stats:
66% (01:46) correct
33% (02:19) wrong based on 6 sessions
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Perimeter of a small rectangular park is 560 feet and measure of its diagonal is 200 feet. What is the area of the park 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
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Re: Perimeter of a small rectangular park is 560 feet and measure of its
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04 Feb 2025, 08:42
04 Feb 2025, 08:42
1
Perimeter of a small rectangular park is 560 feet and measure of its
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17 Feb 2025, 02:27
17 Feb 2025, 02:27
Expert Reply
OFFICIAL EXPLANATION
Let the length \& the breadth of the small rectangular park be L \& B respectively.
As the perimeter of the rectangular park is 560 feet, we get $\(2(L+B)=560 \Rightarrow L+B=280\)$
Also as the diagonal of the park is 200 feet, we get $\(L^2+B^2=200^2=40000\)$ where
$$
\(\begin\mathrm{L}^2+\mathrm{B}^2=(\mathrm{L}+\mathrm{B})^2-2 \mathrm{LB}=(280)^2-2 \mathrm{LB}=78400-2 \mathrm{LB} \\
\)
$$
which gives
\(78400-2 \mathrm{LB}=40000 \Rightarrow \mathrm{LB}=\frac{38400}{2}=19200
\)
Hence the answer is (A).
Let the length \& the breadth of the small rectangular park be L \& B respectively.
As the perimeter of the rectangular park is 560 feet, we get $\(2(L+B)=560 \Rightarrow L+B=280\)$
Also as the diagonal of the park is 200 feet, we get $\(L^2+B^2=200^2=40000\)$ where
$$
\(\begin\mathrm{L}^2+\mathrm{B}^2=(\mathrm{L}+\mathrm{B})^2-2 \mathrm{LB}=(280)^2-2 \mathrm{LB}=78400-2 \mathrm{LB} \\
\)
$$
which gives
\(78400-2 \mathrm{LB}=40000 \Rightarrow \mathrm{LB}=\frac{38400}{2}=19200
\)
Hence the answer is (A).
