A right triangle has an area of 24ft^2. The dimensions of the triangle are increased by a scale factor of 6. What is the area of the new triangle

A right triangle has an area of 24ft2 The dimensions of the triangle are increased by a scale factor of 6 What is the area of the new triangle class=

Respuesta :

Answer:

[tex]864\ ft^2[/tex]

Step-by-step explanation:

we know that

The area of a triangle is equal to

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

[tex]A=24\ ft^2[/tex]

[tex]24=\frac{1}{2}bh[/tex] -------> [tex]48=bh[/tex] ------> equation A

where

b is the base of the triangle

h is the height of the triangle

In this problem the dimensions of the triangle are increased by a scale factor of [tex]6[/tex]

so

the new dimensions of the triangle are

[tex]b=6b, h=6h[/tex]

The new area of the triangle will be

[tex]A1=\frac{1}{2}(6b)(6h)[/tex]

[tex]A1=18bh[/tex] ------> equation B

Substitute equation A in equation B

[tex]A1=18[48]=864\ ft^2[/tex]

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