Find the dimensions of the prayer hall discussed in Section 4.1. (The breadth x satisfies 2x2+x−300=0.)
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Step-by-Step Solution
Step 1: State the given quadratic equation
We are given a quadratic equation that represents the breadth x of the prayer hall. We need to solve this equation to find the value of x.
Step 2: Compare with standard quadratic equation
To solve the quadratic equation, we first identify the coefficients a, b, and c by comparing it with the standard form of a quadratic equation.
Step 3: Identify coefficients
From the given equation 2x2+x−300=0, we can see that a=2, b=1, and c=−300.
Step 4: Apply the quadratic formula
The quadratic formula is used to find the roots of a quadratic equation. We substitute the values of a, b, and c into this formula.
Step 5: Substitute values into the formula
Substitute the identified coefficients a=2, b=1, and c=−300 into the quadratic formula.
Step 6: Simplify the expression under the square root
First, calculate the term inside the square root: 12=1 and 4(2)(−300)=−2400. Then, 1−(−2400)=1+2400=2401. The denominator is 2(2)=4.
Step 7: Calculate the square root
The square root of 2401 is 49. This simplifies the expression further.
Step 8: Solve for x using both positive and negative roots
Now we have two possible values for x: one by taking the positive square root and one by taking the negative square root.
Step 9: Calculate the first possible value of x
For the first root, we use the positive sign. (−1+49) gives 48, and 48 divided by 4 equals 12.
Step 10: Calculate the second possible value of x
For the second root, we use the negative sign. (−1−49) gives −50, and −50 divided by 4 equals −12.5.
Step 11: Determine the valid breadth
Since x represents the breadth of the prayer hall, it cannot be a negative value. Therefore, we discard x=−12.5 and take x=12 metres as the breadth.
Step 12: Find the length of the hall
From Section 4.1 of the textbook, the length of the prayer hall is given as 'one metre more than twice its breadth', so Length =2x+1.
Step 13: Substitute the value of x to find the length
Substitute x=12 metres into the expression for the length to calculate its value.