Question

The area of the quadrilateral bounded by the \(Y\) -axis, the line \(x = 5\) , and the lines \(|x-y|-|x-5|=2\), is

• A. 45
• B. 55
• C. 60
• D. None of Above

Answer 1

The Correct Option is A

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) \( \mathbf{45} \)