20 points the figure shown is a square with a triangular hole cut into one side. the ratio of the height (h) of the triangle to a side length of the square is 7 to 8. the ratio of the base (b) of the triangle to the side length of the square is 1 to 2. if the area of the square is 64 square inches, what is the area of the shaded part of the square? show you work.

Area of shaded part is 50 cm².

Step-by-step explanation:

Since we have given that

Ratio of height of triangle to side length of the square is 7:8.

Let height of triangle be 'h'.

Let the length of square be 'a'.

Let the base of triangle be 'b'.

Ratio of base of triangle to side length of the square is 1:2.

So, Combined ratio will be

          h  :   a   :  b

          7  :    8  

                  4(2   :  1) (to make 'a' as a common part which is 8 )

                = 8      :  4

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   7          :  8        :  4

So, height will be 7x.

Side will be 8x.

Base will be 4x.

Since area of square = 64 cm²

As we know that "Area of square = Side × Side":

So, base becomes 4 inches.

Height becomes 7 inches.

So, Area of triangle becomes

Area of shaded part of the square is

Area of square - Area of triangle

Hence, Area of shaded part is 50 cm².

they can both be solutions depends on the equation

step-by-step explanation:

what is the equation? ?

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have