Question

Ratio of corresponding side of two similiar traingle rs 2:5. If the area of smaller traingle is 64sq .cm what is the area of bigger traingle-​

Answer 1

Appropriate Question :

Ratio of corresponding side of two similiar traingle is 2:5. If the area of smaller traingle is 64sq .cm what is the area of bigger triangle ?

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✾ Given :

• Ratio of corresponding side of two similar triangle is 2:5.

• Area of smaller triangle is 64 sq.cm

❈ To Find :

• The Area of bigger Triangle.

✻ Calculations :

As we know that for similar triangles we use the formulae –

$\boxed{ \red{ \sf{Ratio \: of \: areas \: = ratio \: of \: square \: of \: corresponding \: sides}}} \red{☆}$

(Now, we will change this ratio as a "Fraction.")

$\qquad \qquad \longmapsto \large {\sf{ \frac{Area \: of \: 1st \: triangle}{Area \: of \: 2nd \: triangle} = \frac{ {2}^{2} }{ {5}^{2}}} }$

Now, We have to find the bigger Area.

$\qquad \large{ \sf{ \longmapsto {\dfrac{\text{64} }{\text{Area 2}}=\bigg( \dfrac{\text{4}}{\text{9}} \bigg)^2 }}}$

$\qquad { \mapsto \sf{ Area^{2} \: = \frac{4}{25}}}$

$\qquad \qquad \qquad \sf{ = (64 \times 25) \div 4}$

$\qquad \qquad \qquad \purple{ \boxed{ \sf{ = 400 \: {cm}^{2} }}} \: ✻$

$\therefore$ The Area of bigger triangle is 400 cm².

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