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

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]