Question

If ∆ABC is similar to ∆DEF web that BC = 4 cm, EF = 7 cm sod area of ∆ABC = 144 sq. cm, determine the area of ​

Answer 1

Answer:

◇Given:

BC = 4 cm

EF = 7 cm

ar(ABC) = 144 sq.cm

◇To Find:

ar(DEF)

◇Solution:

Using Theorem Areas of Similar Triangles

If ar(ABC) ~ ar(DEF) then:

$\frac{ar(abc)}{ar(def)} = {( \frac{bc}{ef}) }^{2}$

$\sqrt{ \frac{ar(abc)}{ar(def)} } = \frac{bc}{ef}$

$\sqrt{ \frac{144}{ar(def)} } = \frac{4}{7}$

$\frac{12}{ \sqrt{ar(def)} } = \frac{4}{7}$

$\frac{3}{ \sqrt{ar(def)} } = \frac{1}{7}$

$\sqrt{ar(def)} = 21$

$ar(def) = {(21)}^{2}$

$ar(def) = 441 \: sq.cm$

Therefore, ar(DEF) = 441 sq.cm.

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Answer 2

ar(DEF) = 441 sq.cm

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