Question

Triangle J is shown below. James drew a scaled version of Triangle J using a scale factor of 4 and labeled it Triangle K. What is the area of Triangle K? triangle j: base=5 height=4

Answer 1

The area of triangle K is 16 times greater than the area of triangle J

Step-by-step explanation:

we know that

If Triangle K is a scaled version of Triangle J

then

Triangle K and Triangle J are similar

If two triangles are similar, then the ratio of its areas is equal to the scale factor squared

Let

z -----> the scale factor

Ak ------> the area of triangle K

Aj -----> the area of triangle J

so

z^{2}=\frac{Ak}{Aj}z2=AjAk

we have

z=4z=4

substitute

4^{2}=\frac{Ak}{Aj}42=AjAk

16=\frac{Ak}{Aj}16=AjAk

Ak=16AjAk=16Aj

therefore

The area of triangle K is 16 times greater than the area of triangle J

MARK AS BRAINLIST

Answer 2

If Triangle K is a scaled version of Triangle J

Triangle K and Triangle J are similar

If two triangles are similar, then the ratio of its areas is equal to the scale factor squared

Let,

• z = the scale factor
• Ak = the area of triangle K
• Aj = the area of triangle J

So,

⇒ $z^{2}=\frac{Ak}{Aj}$

⇒ z = 4

⇒ $4^{2}=\frac{Ak}{Aj}$

⇒ $16=\frac{Ak}{Aj}$

⇒ Ak = 16Aj

The area of triangle K is 16 times greater than the area of triangle J.