Question

hamet is putting a concrete sidewalk around her quadrilateral shaped pool. a diagram of the pool, wmyt, and the similarly shaped sidewalk, flkc, are shown, where wmyt ~ flkc, ck = (4x - 1.2) yards (yd), lk = (3.5y + 2.3) yd, fc = 10.8 yd, my = (4y - 2.4) yd, wm = (2.4y - 1.2) yd, wt = 8.1 yd, and ty = (4x - 6.2) yd. solve for x. if necessary, round answers to the nearest tenth.

Explanation:

Step1: Find the scale factor

Since \(WMYT\sim FLKC\), the ratio of corresponding sides is equal. The ratio of \(FC\) to \(WT\) is the scale factor.

$$ \text{Scale factor}=\frac{FC}{WT}=\frac{10.8}{8.1} = 1.333\cdots=\frac{4}{3} $$

Step2: Set up the proportion for \(x\)

Corresponding sides \(CK\) and \(TY\) are in the ratio of the scale factor. So \(\frac{CK}{TY}=\frac{4}{3}\)
Substitute \(CK=(4x - 1.2)\) and \(TY=(4x - 6.2)\)

$$ \frac{4x-1.2}{4x - 6.2}=\frac{4}{3} $$

Cross - multiply:

$$ 3(4x-1.2)=4(4x - 6.2) $$

Step3: Expand the equation

$$ 12x-3.6 = 16x-24.8 $$

Step4: Solve for \(x\)

Subtract \(12x\) from both sides:

$$ -3.6=16x - 12x-24.8 $$

$$ -3.6 = 4x-24.8 $$

Add \(24.8\) to both sides:

$$ 4x=-3.6 + 24.8 $$

$$ 4x=21.2 $$

Divide both sides by \(4\):

$$ x = 5.3 $$

Answer:

\(x = 5.3\)