Question

Draw the graph of equation x=3, x=5 and 2x-y-4=0. Find the area of the quadrilateral formed by the lines and x-axis​

Answer 1

$\texttt{\underline{ \underline{Given:} }}$

x = 3 and 5

$\textsf{Putting \: the \: values \: of \: x \: in \:2x - y - 4 = 0 } \\ \\ \text{Putting \: x = 3}$

2x – y – 4 = 0

$\rightarrow$ 2×3 – y – 4 = 0

$\rightarrow$ 6 – y – 4 = 0

$\rightarrow$ –y = –2

$\rightarrow$ y = 2

$\boxed{ \textbf{y = 2}}$

$\text{Putting \: x = 5}$

2x – y – 4 = 0

$\rightarrow$ 2×5 – y – 4 = 0

$\rightarrow$ 10 – y – 4 = 0

$\rightarrow$ –y = –6

$\rightarrow$ y = 6

$\boxed{ \textbf{y = 6}}$

$\text{area \: of \: formed \: quadrilateral}$

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ABCD is a square $\text{as shown in graph...}$

Area of square = (side)²

$\rightarrow$A = 2 × 2

$\rightarrow$A = 4 cm²

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Area of triangle = 1/2 × b × h

$\rightarrow$A = 1/2 × 2 × 4

$\rightarrow$A = 4 cm²

_________________________________

Area of quadrilateral = Sum of area of square and triangle .

$\rightarrow$A = 4 cm² + 4 cm²

$\rightarrow$A = 8 cm²

$\boxed{ \text{Area of quadrilateral = 8 sq. cm}}$

Answer 2

Answer:

x = 3 and 5

2x – y – 4 = 0

2×3 – y – 4 = 0

6 – y – 4 = 0

–y = –2

y = 2

2x – y – 4 = 0

2×5 – y – 4 = 0

10 – y – 4 = 0

–y = –6

y = 6

________________________________

ABCD is a square

Area of square = (side)²

A = 2 × 2

A = 4 cm²

_________________________________

Area of triangle = 1/2 × b × h

A = 1/2 × 2 × 4

A = 4 cm²

_________________________________

Area of quadrilateral = Sum of area of square and triangle .

A = 4 cm² + 4 cm²

A = 8 cm²