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The dimensions of a triangle are shown below. If the height of the triangle is increased by the factor of 4, which statement will be true about the area of the triangle?


A. the area will increase by a factor of 2.
B. the area will increase by a factor of 4.
C. the area will increase by a factor of 8
D. the area will not change

Respuesta :

calculista

Answer:

Option B. The area will increase by a factor of 4

Step-by-step explanation:

we know that

The area of triangle is equal to

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

where

b is the base of triangle

h is the height of triangle

If the height of the triangle is increased by the factor of 4

then

The new area of the triangle will be

[tex]Anew=\frac{1}{2}b(4h)[/tex]

[tex]Anew=4[\frac{1}{2}bh][/tex]

[tex]Anew=4[A][/tex]

The new area is 4 times the original area

therefore

The area will increase by a factor of 4