Question

lt 1d – i can solve problems using triangle proportionality
the figures are similar. find the value of x.
△stu ~ △hgf
16.
diagram: △hgf with sides 4, 3; △stu with sides 12, 2x - 3
x = ____

1. the...

Explanation:

Step1: Set up proportion for similar triangles

Since \(\triangle STU \sim \triangle HGF\), the corresponding sides are proportional. So \(\frac{ST}{HG}=\frac{TU}{GF}\). Here, \(ST = 12\), \(HG = 4\), \(TU = 2x - 3\), \(GF = 3\). Thus, \(\frac{12}{4}=\frac{2x - 3}{3}\).

Step2: Simplify and solve for x

Simplify \(\frac{12}{4}\) to get \(3\). So the equation becomes \(3=\frac{2x - 3}{3}\). Multiply both sides by \(3\): \(3\times3 = 2x - 3\), which is \(9 = 2x - 3\). Add \(3\) to both sides: \(9 + 3 = 2x\), so \(12 = 2x\). Divide both sides by \(2\): \(x=\frac{12}{2}=6\).

Answer:

\(6\)