Question

What are a) the ratio of the perimeter’s b) and the ratio of areas of the larger figure to the smaller figure?

Answer 1

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Answer 2

a) We have been given two similar figures and we have to find ratio of perimeters of these figures.

Let a be given side of larger figure and b be the given side of smaller figure. Let $p_{1} \text{ and } p_{2}$ be the perimeters of two figures and $A_{1} \text{ and } A_{2}$ be the areas of the two figures.

We know that perimeters of two similar figures are in the ratio of corresponding sides.

$\frac{p_{1}}{p_{2}}=\frac{a}{b}$

We have been given, $a=26\text{ and }b=6$

Therefore, upon substituting these values in the above equation, we get

$\frac{p_{1}}{p_{2}}=\frac{26}{6}$

$\frac{p_{1}}{p_{2}}=\frac{13}{3}$

(b)

Further we know that areas of two similar figures are in the ratio of squares of corresponding sides.

$\frac{A_{1}}{A_{2}}=\frac{a^{2}}{b^{2}}\\ \frac{A_{1}}{A_{2}}=\frac{26^{2}}{6^{2}}\\ \frac{A_{1}}{A_{2}}=\frac{676}{36}\\ \frac{A_{1}}{A_{2}}=\frac{169}{9}$

Therefore, first option is the correct answer.