Question

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

Answer 1

Answer:

Hint: Here, mark the points on the graph, and join the lines to form a triangle. Using distance formula, find the length of three sides. Add the three lengths to find the perimeter of the triangle.

Complete step-by-step answer:

Let the points are A (0, 4), O (0, 0) and B (3, 0).

For length OA,

For length OA,Using distance formula,

For length OA,Using distance formula, ⇒OA=(0−0)2+(4−0)2−−−−−−−−−−−−−−−√=16−−√=4⇒OA=(0−0)2+(4−0)2=16=4 units

For length OA,Using distance formula, ⇒OA=(0−0)2+(4−0)2−−−−−−−−−−−−−−−√=16−−√=4⇒OA=(0−0)2+(4−0)2=16=4 unitsFor length OB,ss

For length OA,Using distance formula, ⇒OA=(0−0)2+(4−0)2−−−−−−−−−−−−−−−√=16−−√=4⇒OA=(0−0)2+(4−0)2=16=4 unitsFor length OB,ssUsing distance formula,

For length OA,Using distance formula, ⇒OA=(0−0)2+(4−0)2−−−−−−−−−−−−−−−√=16−−√=4⇒OA=(0−0)2+(4−0)2=16=4 unitsFor length OB,ssUsing distance formula, ⇒OB=(3−0)2+(0−0)2−−−−−−−−−−−−−−−√=9–√=3⇒OB=(3−0)2+(0−0)2=9=3 units

For length OA,Using distance formula, ⇒OA=(0−0)2+(4−0)2−−−−−−−−−−−−−−−√=16−−√=4⇒OA=(0−0)2+(4−0)2=16=4 unitsFor length OB,ssUsing distance formula, ⇒OB=(3−0)2+(0−0)2−−−−−−−−−−−−−−−√=9–√=3⇒OB=(3−0)2+(0−0)2=9=3 unitsFor length AB,

For length OA,Using distance formula, ⇒OA=(0−0)2+(4−0)2−−−−−−−−−−−−−−−√=16−−√=4⇒OA=(0−0)2+(4−0)2=16=4 unitsFor length OB,ssUsing distance formula, ⇒OB=(3−0)2+(0−0)2−−−−−−−−−−−−−−−√=9–√=3⇒OB=(3−0)2+(0−0)2=9=3 unitsFor length AB,Using distance formula,

For length OA,Using distance formula, ⇒OA=(0−0)2+(4−0)2−−−−−−−−−−−−−−−√=16−−√=4⇒OA=(0−0)2+(4−0)2=16=4 unitsFor length OB,ssUsing distance formula, ⇒OB=(3−0)2+(0−0)2−−−−−−−−−−−−−−−√=9–√=3⇒OB=(3−0)2+(0−0)2=9=3 unitsFor length AB,Using distance formula, ⇒AB=(0−3)2+(4−0)2−−−−−−−−−−−−−−−√=9+16

AB=(0−3)2+(4−0)2−−−−−−−−−−−−−−−√=9+16−−−−−√=25−−√=5⇒AB=(0−3)2+(4−0)2=9+16=25=5 units

AB=(0−3)2+(4−0)2−−−−−−−−−−−−−−−√=9+16−−−−−√=25−−√=5⇒AB=(0−3)2+(4−0)2=9+16=25=5 unitsPerimeter of triangle ABC, P=AB+BC+ACP=AB+BC+AC

AB=(0−3)2+(4−0)2−−−−−−−−−−−−−−−√=9+16−−−−−√=25−−√=5⇒AB=(0−3)2+(4−0)2=9+16=25=5 unitsPerimeter of triangle ABC, P=AB+BC+ACP=AB+BC+ACP = 3 units + 4 units + 5 units = 12 units

AB=(0−3)2+(4−0)2−−−−−−−−−−−−−−−√=9+16−−−−−√=25−−√=5⇒AB=(0−3)2+(4−0)2=9+16=25=5 unitsPerimeter of triangle ABC, P=AB+BC+ACP=AB+BC+ACP = 3 units + 4 units + 5 units = 12 unitsSo, the correct answer is “12 units

Note: In these types of questions, draw the figure on a graph to understand the question geometrically.One important thing about this question is that we can find hypotenuse using Pythagoras theorem as one angle in this question is right angle. Here, (0, 4) means length of this point from origin is 4 units and (3, 0) means length of this point from the origin is 3 units. Using these two lengths and Pythagoras theorem we can find the length of the third side. Add them to get the perimeter of the triangle.

Answer 2

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