Question

1. if \\( \triangle sde \sim \triangle swt \\), find the value of \\( x \\).

Explanation:

Step1: Use the property of similar triangles

Since \(\triangle SDE\sim\triangle SWT\), the ratios of corresponding sides are equal. That is \(\frac{SE}{ST}=\frac{SD}{SW}\).
We know \(SE = 40\), \(ST=4x - 3\), \(SD = 56\), and \(SW=5x + 3\).
So, \(\frac{40}{4x-3}=\frac{56}{5x + 3}\).

Step2: Cross - multiply

Cross - multiplying gives us \(40(5x + 3)=56(4x - 3)\).
Expand both sides:

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Step3: Solve for \(x\)

Move the \(x\) terms to one side and the constants to the other side:
\(224x-200x=120 + 168\).
\(24x=288\).
Divide both sides by \(24\): \(x=\frac{288}{24}=12\).

Answer:

\(12\)