Question

If the sides of a triangle are doubled then its area

Answer 1

Step-by-step explanation:

The area of a triangle is given by (1/2)*base*height. If the length ofthe sides becomes double so does the height. As base and height are becoming double the new area is 4 times the originalarea. When the length of the sides of a triangle double, thearea becomes quadruple.

Answer 2

Answer: Its area gets four times the initial area of the triangle.

Step-by-step explanation:

For a right angled triangle, the area is given by,

A = $\frac{1}{2}$*base*height

where, base is the line segment on which the perpendicular is standing and the height id the perpendicular length.

Now, if the sides of the triangles are doubled, then lets find out the area of the triangle.

Step 1: Let AB, BC,AC are the three sides of the right angled triangle ABC such that BC is the base measuring b units, AB is the height measuring a units and AC is the hypotenuse measuring h units.

So the are of the triangle ABC is given by,

A = $\frac{1}{2}$*b*a

Step 2: On doubling the sides of the trianlge, we have 2a and 2b as the sides. So the area becomes,

A' = $\frac{1}{2}$*2b*2a = 4*$\frac{1}{2}$*b*a = 4*A

So we see that the area becomes four times the initial area that we got before doubling the sides of the triangle.

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