Similar Figures Math Example 2

Follow the full solution, then compare it with the other examples linked below.

hard

Rectangle

ABCD \sim

Rectangle

EFGH

with

AB = 8

BC = 5

EF = 12

. Find

FG

and the ratio of areas.

1
Scale factor: $k = \dfrac{EF}{AB} = \dfrac{12}{8} = \dfrac{3}{2}$ .
2
Since $BC$ corresponds to $FG$ : $FG = 5 \times \dfrac{3}{2} = 7.5$ .
3
Area of $ABCD = 8 \times 5 = 40$ ; Area of $EFGH = 12 \times 7.5 = 90$ .
4
Ratio of areas $= \dfrac{90}{40} = \dfrac{9}{4} = k^2 = \left(\dfrac{3}{2}\right)^2$ . ✓

Answer

FG = 7.5

; area ratio is

\dfrac{9}{4}

In similar figures, linear dimensions scale by

k

while areas scale by

k^2

. Here

k = \frac{3}{2}

, so the area ratio is

\frac{9}{4}

. This quadratic relationship between linear and area scaling is a fundamental property of similarity.

About Similar Figures

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