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A certain triangle has a base (x) and a height (v). a new triangle is created by tripling the length of the base and quadrupling the height. how does the area of the second triangle compare to the area of the first?
a. 3 times larger
b. 4 times larger
c. 6 times larger
d. 12 times larger
e. 7 times larger

Respuesta :

The area of new triangle with base '3b'and height '6h' is 6 times larger than the area of original triangle with base 'b' and height 'h'.

The correct option is (c)

What is area of triangle?

The area of a triangle is half the product of its base and height.

Area= [tex]\frac{1}{2} * b * h\\[/tex]

Let us consider the base 'b' and the height 'h'.

The Area of triangle will be,

= [tex]\frac{1}{2} * b * h\\[/tex]

=[tex]\frac{1}{2} bh[/tex]

Now, if the base is tripled and height is quadrupling.

Then, new base = 3b and new height =4h

So, Area of new Triangle =[tex]\frac{1}{2} * (3b) * (4h)[/tex]

                                          = [tex]\frac{12}{2} bh[/tex]

                                          = 6 bh

                                          = 6 times larger than the original triangle.

Hence, the area of new triangle will be 6 times larger the area of the original triangle.

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