Question

Calculate the area bounded by the line x + y = 10 and both the co-ordinate axes.​

Answer 1

$\large\underline{\sf{Solution-}}$

Given equation of line is

$\red{ \boxed{ \rm :\longmapsto\:\rm{ \: x + y = 10}}}$

Substituting 'x = 0' in the given equation, we get

$\rm :\longmapsto\:0 + y = 10$

$\rm :\longmapsto\:y = 10$

Substituting 'x = 5' in the given equation, we get

$\rm :\longmapsto\:5 + y = 10$

$\rm :\longmapsto\:y = 10 - 5$

$\rm :\longmapsto\:y = 5$

Substituting 'x = 10' in the given equation, we get

$\rm :\longmapsto\:10 + y = 10$

$\rm :\longmapsto\:y = 10 - 10$

$\rm :\longmapsto\:y = 0$

Hᴇɴᴄᴇ,

➢ Pair of points of the given equation are shown in the below table.

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf 10 \\ \\ \sf 5 & \sf 5 \\ \\ \sf 10 & \sf 0 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points (0 , 10), (5 , 5) & (10 , 0)

➢ See the attachment graph.

Now,

From graph, we conclude that OAB is the required region bounded by the line x + y = 10 with both the coordinates axis.

So,

Area of triangle OAB

= 1/2 × OA × OB

= 1/2 × 10 × 10

= 50 sq.units.

Remark :-

The area bounded by the line ax + by + c = 0 with coordinate axis is given by

$\red{ \boxed{ \bf{ \: Area_{\triangle} = \frac{ {c}^{2} }{2 \: |a| \: |b| } }}}$