Dimensions of a Garden Arif’s backyard is 20 meters by 30 meters. He wants to put a flower garden in the middle of the backyard, leaving a strip of grass of uniform width around the flower garden. To be happy, he must have 184 square meters of grass. Under these conditions, what will the length and width of the garden be?
To calculate: The length and width of the garden if the length and width of the backyard are
Answer to Problem 57E
Solution:
The length and width of the garden are
Explanation of Solution
Given:
The length and width of the backyard are
Formula used:
the length and width of the backyard as
And,
The quadratic formula to solve the quadratic equation
Here,
Calculation:
Consider the length and width of the backyard as
Substitute
Consider the width of the grass as
Similarly, from Figure 1, calculate the area of the garden.
Now, from Figure 1, it is clear that when the area of the garden is subtracted from the area of the backyard, then it will give the area of the grass. Calculate the area of the grass.
Substitute
Further, substitute
Write the equation in standard form and solve by factoring.
Use the quadratic formula to solve the quadratic equation.
Here,
Substitute 1 for
Further, solve.
Thus, solutions of the above equation are,
Or,
Since the width of the backyard is
Substitute
Similarly, calculate the width of the garden.
Substitute
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