two right triangles are similar. the of the larger triangle is 4 times as long as the base of the smaller triangle. the height of the longer triangle is 16cm. the area of the smaller triangle is 6cm^2. What is the area of the long triangle?

6*4*4=128

The relationship between the perimeter of the image and the perimeter of the original shape

To find the area of the larger triangle, we need to know the lengths of its base and height.

Given that the larger triangle is similar to the smaller triangle, we can use this information to set up a proportion.

Let's define the base of the smaller triangle as 'b' and the base of the larger triangle as '4b'. The height of the larger triangle is given as 16 cm.

The proportion we can set up is:

(base of larger triangle) / (base of smaller triangle) = (height of larger triangle) / (height of smaller triangle)

Substituting the known values:

4b / b = 16 cm / ?

By cross-multiplying, we get:

4b * ? = b * 16 cm

Simplifying the equation:

4b? = 16b

Dividing both sides by 4b:

? = 16b / 4b

Simplifying:

? = 4 cm

Therefore, the height of the smaller triangle is 4 cm.

Now that we know the base and height of the larger triangle, we can calculate its area:

Area = (base * height) / 2

Area = (4b * 16 cm) / 2

Area = 32b cm^2

To find the value of 'b', we can use the area of the smaller triangle:

6 cm^2 = (b * 4 cm) / 2

12 cm^2 = 4b cm

Dividing both sides by 4:

3 cm^2 = b cm

Now substitute the value of 'b' into the formula for the area of the larger triangle:

Area = 32 * (3 cm^2)

Area = 96 cm^2

Therefore, the area of the larger triangle is 96 cm^2.