Question

figure a is a scale image of figure b.
figure a
figure b
figure a maps to figure b with a scale factor of \frac{2}{7}.
what is the value of x?

Explanation:

Step1: Set up the proportion

Since Figure A is a scale image of Figure B with scale factor \(\frac{2}{7}\), we have \(\frac{\text{Length in Figure A}}{\text{Length in Figure B}}=\frac{2}{7}\). Here, length in Figure A is \(x\) and in Figure B is \(12\), so \(\frac{x}{12}=\frac{2}{7}\).

Step2: Solve for \(x\)

Cross - multiply: \(7x = 2\times12\). Then \(7x=24\). Divide both sides by \(7\): \(x=\frac{24}{7}= 42\).

Answer:

\(42\)