The diagonal and one side of a rectangular plot are 289 m and 240 m respectively . Find the other side :

Options

A. 237 m
B. 181 m
C. 161 m
D. 159 m

Answer

To find the other side of the rectangular plot, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (the diagonal in this case) is equal to the sum of the squares of the other two sides.

Let's denote:
- The length of the diagonal (hypotenuse) as \( d = 289 \, m \)
- One side (let's say width) as \( a = 240 \, m \)
- The other side (let's say length) as \( b \) (which we need to find)

According to the Pythagorean theorem:
\[ d^2 = a^2 + b^2 \]

### Step 1: Substitute the known values into the equation.
\[ 289^2 = 240^2 + b^2 \]

### Step 2: Calculate \( 289^2 \) and \( 240^2 \).
\[ 289^2 = 83521 \]
\[ 240^2 = 57600 \]

### Step 3: Substitute these values back into the equation.
\[ 83521 = 57600 + b^2 \]

### Step 4: Rearrange the equation to solve for \( b^2 \).
\[ b^2 = 83521 - 57600 \]

### Step 5: Perform the subtraction.
\[ b^2 = 25921 \]

### Step 6: Take the square root of both sides to find \( b \).
\[ b = \sqrt{25921} \]
\[ b = 161 \, m \]

### Conclusion:
The other side of the rectangular plot is \( 161 \, m \).

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