Question

Find the area of a triangle formed by line 3x+5y=15 with coordinate axes. *

15

7.5

5

3

​

Answer 1

Answer:

Step-by-step explanation:

When x = 0, y = 3, and when y= 0, x= 5 for 3x+5y = 15

this means it's a triangle with base = 5 (on x axis)

and height = 3 (on y axis)

therefore area = 1/2*5*3 = 7.5

Answer 2

Given,

Line 3x + 5y = 15.

To find,

Area of the triangle formed by given line with coordinate axes.

Solution,

This problem can be solved simply by following the below steps.

To find the area of the triangle formed by the given line and coordinate axes, we first need to find the lengths of sides, which can be found using coordinates of points where the line intersects the axes.

From the given equation, we can find the intersection of the line with the x-axis, by substituting y = 0.

So, 3x + 5(0) = 15

⇒ 3x = 15

⇒ x = 5.

It means at (5, 0), the line intersects the x-axis.

Similarly, put x = 0 in the equation, to find the coordinates of the intersecting point on the y-axis. So,

3(0) + 5y =15

⇒ 5y = 15

⇒ y = 3.

Hence, the line intersects the y-axis at (0, 3).

Now, the length of the triangle on the y-axis can be considered as the height (h) and base (b) on the x-axis. Also, it will be a right triangle since, coordinate axes intersect at a right angle at origin O(0, 0).

So, here, h = 3 units, b = 5 units.

We can apply

$A= \frac{1}{2} *b*h$ to find the area.

⇒ $A=\frac{1}{2} *5*3$

⇒ $A=\frac{15}{2}$

⇒ $A = 7.5\hspace{3} sq \hspace{3}units.$

Therefore, the area of the triangle formed by line 3x + 5y = 15 with coordinate axes will be 7.5 square units.