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2 years ago

the perimeter of a rectangular campsite is 64m and its area is 207m^2. find the length and breadth of the campsite

Mathematics

1 answer:

NNADVOKAT [17]2 years ago

4 0

Answer:

The length is $23\ m$ and the breadth is $9\ m$

Step-by-step explanation:

Let

x ----> the length of a rectangular campsite

y ----> the breadth of a rectangular campsite

we know that

The perimeter of a rectangle is equal to

$P=2(x+y)$

$P=64\ m$

$64=2(x+y)$

$32=(x+y)$

$y=32-x$ ------> equation A

The area of a rectangle is equal to

$A=xy$

$A=207\ m^{2}$

$207=xy$ -----> equation B

substitute equation A in equation B

$207=x(32-x)\\\\207=32x-x^{2}\\\\x^{2}-32x+207=0$

Solve the quadratic equation by graphing

The solution is $x=23\ m$ ( I assume that the length is greater than the breadth)

see the attached figure

Find the value of y

$y=32-23=9\ m$

therefore

The length is $23\ m$ and the breadth is $9\ m$

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