Question:
The area of the quadrilateral bounded by the \(Y\) -axis, the line \(x = 5\) , and the lines \(|x-y|-|x-5|=2\), is
The area of the quadrilateral bounded by the \(Y\) -axis, the line \(x = 5\) , and the lines \(|x-y|-|x-5|=2\), is
Updated On: Jan 13, 2026
- 45
- 55
- 60
- None of Above
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The Correct Option is A
Solution and Explanation
To find: Area of quadrilateral \( ABDE \)
Approach: The quadrilateral \( ABDE \) is made up of:
- Rectangle \( ABCD \)
- Triangle \( \triangle CDE \)
So, Area of \( ABDE = \) Area of rectangle \( ABCD \) + Area of triangle \( \triangle CDE \)
Step 1: Area of rectangle \( ABCD \)
Length = \( 7 - 3 = 4 \) units
Breadth = \( 5 \) units
Area = \( \text{Length} \times \text{Breadth} = 4 \times 5 = 20 \) square units
Step 2: Area of triangle \( \triangle CDE \)
Given: Base = \( 10 \) units, Height = \( 5 \) units
Area = \( \frac{1}{2} \times \text{Base} \times \text{Height} = \frac{1}{2} \times 10 \times 5 = 25 \) square units
Step 3: Total Area of Quadrilateral \( ABDE \)
\( = 20 + 25 = \mathbf{45} \) square units
Final Answer: (A) \( \mathbf{45} \)
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