Leia cuts congruent triangular patches with an area of 35 square centimeters from a rectangular piece of fabric that is 14 centimeters long and 10 centimeters wide. How many of the patches can Leia cut from 27 pieces of the fabric?

Leia can cut 108 patches from 27 pieces of fabric.

Step-by-step explanation:

Given:

Area of triangular patches =

Length of rectangular piece of fabric = 14 cm

Width of rectangular piece of fabric = 10 cm

We need to find number of patches Leia can cut from 27 pieces of fabric.

Solution:

First we will find the area of rectangular piece of fabric.

Now we know that;

Area of rectangle is given by length times width.

framing in equation form we get;

area of rectangular piece of fabric =

Now we will find the number of patches triangular patches cut from each piece of rectangular fabric.

number of patches triangular patches cut from each piece of rectangular fabric can be calculated by dividing area of rectangular piece of fabric from Area of triangular patches.

framing in equation form we get;

Number of patch from each fabric  =

Hence 4 triangular patches can be cut form each rectangular  piece of fabric.

Now we will find the number of triangular patches can be cut form 27 rectangular  piece of fabric.

Now we know that;

1 piece of rectangular fabric = 4 triangular patches can be cut

27 piece of rectangular fabric = Number of triangular patches can be cut form 27 piece of rectangular fabric.

Using Unitary method we get;

Number of triangular patches can be cut form 27 piece of rectangular fabric  =

Hence Leia can cut 108 patches from 27 pieces of fabric.