Question

this triangle is a scaled copy. it was scaled by a factor of 1/2. suppose you want to scale it back to its original size. what are the base and height of the original triangle? to scale back to the original, use a scale factor of 2.

Explanation:

Step1: Recall the scale - factor relationship

If the scaled - copy is obtained by a scale factor of $k$, to get back to the original, we use the reciprocal scale factor. Here $k = \frac{1}{2}$, so to go back to the original, we use a scale factor of 2.

Step2: Calculate the original base

The base of the scaled - copy is 20 cm. Multiply the base of the scaled - copy by the scale factor 2. Let $b_{original}$ be the base of the original triangle and $b_{scaled}=20$ cm. Then $b_{original}=2\times b_{scaled}=2\times20 = 40$ cm.

Step3: Calculate the original height

The height of the scaled - copy is 10 cm. Multiply the height of the scaled - copy by the scale factor 2. Let $h_{original}$ be the height of the original triangle and $h_{scaled}=10$ cm. Then $h_{original}=2\times h_{scaled}=2\times10 = 20$ cm.

Answer:

Base: 40 cm
Height: 20 cm