Question

The area of two similar triangles ABC and DEF are 144cm.sq and 81cm .sq , respectively. if the longest side of larger triangle ABC be 36 cm, then find the longest side of the similar triangle DEF.

Answer 1

Answer:

The longest side of the similar triangle DEF = 27

Step-by-step explanation:

Theorem : The ratio of areas of similar triangle is equal to the ratio of square of similar sides

It is given that,

The area of two similar triangles ABC and DEF are 144cm.sq and 81cm .sq

And  if the longest side of larger triangle ABC be 36 cm,

Let 'X' be the longest side of DEF.

By the theorem we can write,

(longest side of DEF)^2/(longest side of ABC)^2 = (Area of DEF)/(Area of ABC)

$\frac{X^{2}}{36^{2}}=\frac{81}{144}$

${X^{2=\frac{81*36*36}{144}$

$X^{2=729}$

Therefore, $X=\sqrt{729}$

X = 27

Therefore the longest side of the similar triangle DEF = 27

Answer 2

Answer:

27

Step-by-step explanation:

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