Calculate the area, in square units, of the triangle formed by the straight line 3x + 4y -… — JAMB UTME

Calculate the area, in square units, of the triangle formed by the straight line $3x + 4y - 24 = 0$ and the coordinate axes.

Cevap: 24 square units

The area of the triangle formed by the line and the coordinate axes is 24 square units.

To find the area of the triangle bounded by a straight line and the coordinate axes, determine the magnitude of the

x

-intercept and

y

-intercept. Setting

y = 0

3x + 4y - 24 = 0

gives

x = 8

. Setting

x = 0

gives

y = 6

. The vertices of the right triangle are at

(0,0)

(8,0)

, and

(0,6)

. The area is calculated as

\frac{1}{2} \times 8 \times 6 = 24

square units.

Find the

x

-intercept of the straight line

x = 8

, corresponding to the point

(8, 0)

Setting

y = 0

determines where the line crosses the horizontal axis

Find the

y

-intercept of the straight line

y = 6

, corresponding to the point

(0, 6)

Setting

x = 0

determines where the line crosses the vertical axis

Compute the area of the right-angled triangle formed with the origin

(0,0)

\text{Area} = \frac{1}{2} \times 8 \times 6 = 24

The coordinate axes are perpendicular, making the triangle right-angled with base length 8 and height 6

Area of a triangle bounded by a straight line and the coordinate axes

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