Question

Quadrilateral BCDE is similar to quadrilateral FGHI. Find the measure of side GH.
Round your answer to the nearest tenth if necessary.

Answer 1

The question illustrates equivalent ratios, because both quadrilaterals are similar.

The length of GH is 35.1 units

From the question (see attachment), the corresponding sides are:

• CD and GH
• DE and HI

So, we have:

$\mathbf{CD : DE = GH : HI}$

The side lengths are:

$\mathbf{HI = 51}$

$\mathbf{CD = 11}$

$\mathbf{DE = 16}$

So, we have:

$\mathbf{11 : 16 = GH : 51}$

Express as fractions

$\mathbf{\frac{11 }{ 16} = \frac{GH }{ 51}}$

Make GH the subject

$\mathbf{GH =51 \times \frac{11 }{ 16}}$

$\mathbf{GH =35.1}$

Hence, the length of GH is 35.1 units

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