Question

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the triangles are similar.
what is the value of x?
enter your answer in the box.
x =
diagram of two right triangles, larger with legs 3x+8 and 15, hypotenuse 25; smaller with legs 4 and 3, hypotenuse 5

Explanation:

Step1: Set up proportion for similar triangles

Since the triangles are similar, the ratios of corresponding sides are equal. The hypotenuses are 25 and 5, the bases are 15 and 3, and the heights are \(3x + 8\) and 4. The ratio of hypotenuses is \(\frac{25}{5}=5\), and the ratio of bases is \(\frac{15}{3}=5\). So the ratio of heights should also be 5. Thus, \(\frac{3x + 8}{4}=5\).

Step2: Solve the equation for x

Multiply both sides by 4: \(3x + 8 = 5\times4\)
Simplify right side: \(3x + 8 = 20\)
Subtract 8 from both sides: \(3x = 20 - 8\)
Simplify: \(3x = 12\)
Divide by 3: \(x=\frac{12}{3}\)
Simplify: \(x = 4\)

Answer:

4