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The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is

  1. 5 units

  2. 12 units

  3. 11 units

  4. 7 + 5\sqrt{5} units

Coordinate Geometry

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Answer

Let A(0, 4), B(0, 0) and C(3, 0) be the vertices of the triangle.

The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is? Coordinate Geometry, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.

By distance formula,

d=(x2−x1)2+(y2−y1)2∴AB=(0−0)2+(0−4)2=0+(−4)2=16=4 units.∴BC=(3−0)2+(0−0)2=32+0=9=3 units∴AC=(3−0)2+(0−4)2=32+(−4)2=9+16=5 units.d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2} \\[1em] \therefore AB = \sqrt{(0 - 0)^2 + (0 - 4)^2} \\[1em] = \sqrt{0 + (-4)^2} \\[1em] = \sqrt{16} \\[1em] = 4 \text{ units}. \\[1em] \therefore BC = \sqrt{(3 - 0)^2 + (0 - 0)^2} \\[1em] = \sqrt{3^2 + 0} \\[1em] = \sqrt{9} \\[1em] = 3 \text{ units} \\[1em] \therefore AC = \sqrt{(3 - 0)^2 + (0 - 4)^2} \\[1em] = \sqrt{3^2 + (-4)^2} \\[1em] = \sqrt{9 + 16} \\[1em] = 5 \text{ units}.

Perimeter = AB + BC + AC = 4 + 3 + 5 = 12 units.

Hence, Option 2 is the correct option.

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