Question

1. if δdef ~ δjkl, find kl. image of two triangles: δdef with de = 10, ef = x + 11; δjkl with jk = 25, kl (or corresponding side) = 6x + 3

Explanation:

Step1: Identify corresponding sides

Since \(\triangle DEF \sim \triangle JKL\), their corresponding sides are proportional. So, \(\frac{DE}{JK}=\frac{EF}{KL}\). Here, \(DE = 10\), \(JK = 25\), \(EF=x + 11\), \(KL=6x + 3\).

Step2: Set up proportion equation

\(\frac{10}{25}=\frac{x + 11}{6x+3}\)
Cross - multiply: \(10(6x + 3)=25(x + 11)\)

Step3: Expand both sides

Left side: \(10\times6x+10\times3 = 60x+30\)
Right side: \(25\times x+25\times11=25x + 275\)
So, \(60x+30 = 25x+275\)

Step4: Solve for x

Subtract \(25x\) from both sides: \(60x-25x+30=25x - 25x+275\), \(35x+30 = 275\)
Subtract 30 from both sides: \(35x+30 - 30=275 - 30\), \(35x=245\)
Divide both sides by 35: \(x=\frac{245}{35}=7\)

Step5: Find KL

Substitute \(x = 7\) into \(KL = 6x+3\)
\(KL=6\times7 + 3=42 + 3=45\)

Answer:

45