Question

find the value of x that makes \\( \triangle big - \triangle mop \\). figure is not drawn to scale. x =

Explanation:

Step1: Use the property of similar triangles

For similar triangles \(\triangle BIG\) and \(\triangle MOP\), the ratios of corresponding sides are equal. So, \(\frac{BG}{MP}=\frac{IG}{OP}\).
Given \(BG = 12\mathrm{cm}\), \(MP=18\mathrm{cm}\), \(IG = 10\mathrm{cm}\), and \(OP=(2x + 7)\mathrm{cm}\).
Substitute these values into the proportion: \(\frac{12}{18}=\frac{10}{2x+7}\).

Step2: Cross - multiply

Cross - multiplying gives \(12\times(2x + 7)=18\times10\).
Expand the left side: \(24x+84 = 180\).

Step3: Solve for \(x\)

Subtract 84 from both sides: \(24x=180 - 84\), so \(24x=96\).
Divide both sides by 24: \(x=\frac{96}{24}\).

Answer:

\(x = 4\)