Question

sp# 12 8. if \\( \triangle sde \sim \triangle swt \\), find wt.
sp# 9 9. if \\( \triangle gfe \sim \triangle ghj \\), find the value of x.

Explanation:

Step1: Use the property of similar triangles

For similar triangles, the ratios of corresponding sides are equal. So, \(\frac{4x - 3}{5x + 3}=\frac{40}{56}\).

Step2: Simplify the right - hand side ratio

Simplify \(\frac{40}{56}\) to \(\frac{5}{7}\). The equation becomes \(\frac{4x - 3}{5x + 3}=\frac{5}{7}\).

Step3: Cross - multiply

Cross - multiplying gives \(7(4x - 3)=5(5x + 3)\).

Step4: Expand both sides

Expand: \(28x-21 = 25x + 15\).

Step5: Solve for \(x\)

Subtract \(25x\) from both sides: \(28x-25x-21=25x - 25x+15\), which simplifies to \(3x-21 = 15\). Then add \(21\) to both sides: \(3x=15 + 21\), so \(3x=36\). Divide both sides by \(3\): \(x = 12\).

Answer:

\(x = 12\)