Question

figure a is a scale image of figure b. figure a (with side ( x )) and figure b (with side 5) are shown. figure a maps to figure b with a scale factor of ( 2\frac{1}{2} ). what is the value of ( x )?

Explanation:

Step1: Recall scale factor formula

When a figure is scaled to another, the length of the scaled figure (Figure B) is equal to the length of the original figure (Figure A) multiplied by the scale factor. So, \( \text{Length of B} = \text{Length of A} \times \text{Scale Factor} \). Here, we know the length of B is 5, scale factor is \( 2\frac{1}{2}=\frac{5}{2} \), and we need to find \( x \) (length of A). So we can rearrange the formula to \( x=\frac{\text{Length of B}}{\text{Scale Factor}} \).

Step2: Substitute values and calculate

Substitute Length of B = 5 and Scale Factor = \( \frac{5}{2} \) into the formula: \( x = \frac{5}{\frac{5}{2}} \). Dividing by a fraction is multiplying by its reciprocal, so \( x = 5\times\frac{2}{5} \). The 5s cancel out, giving \( x = 2 \).

Answer:

2