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Find the length of the longest side of the triangle formed by the line $3 x + 4 y = 12$ with the coordinate axes.

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3 units

4 units

5 units

2 units

answer is C.

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Detailed Solution

It is given that
Triangle formed by the line

3 x + 4 y = 12

with the coordinate axes.
We know that if the two sides of the given triangle are the coordinate axes the resulting triangle is right-angled.
And the longest side in the right-angled triangle is the hypotenuse.
So, first find out the

x and y

-intercepts of the line

3 x + 4 y = 12

At y = 0, ⇒ x = 123 = 4 ∴ (4, 0) And At x = 0, ⇒ y = 124 = 3 ∴ (0, 3)

Since,
The distance between any two points in a Cartesian plane

M a, b, N c, d

is given by

M N = (c − a) 2 + (d − b) 2

.
Then,
From the graph,
Thus, the length of the hypotenuse AB is,

A B = (0 − 4) 2 + (3 − 0) 2 = 16 + 9 = 25 = 5

Therefore, length of the longest side of the triangle is 5 units.
Hence, option (3) is correct.

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