Corresponding sides of two similar triangles | vedclass

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(B) Given,the ratio of corresponding sides of two similar triangles is $2:3$.Let the area of the smaller triangle be $A_1 = 48 \, cm^2$ and the area o

Vedclass · Accepted Answer

$108$

Vedclass · Answer

(B) Given,the ratio of corresponding sides of two similar triangles is $2:3$.Let the area of the smaller triangle be $A_1 = 48 \, cm^2$ and the area of the larger triangle be $A_2$.According to the theorem of the area of similar triangles,the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.$\frac{A_1}{A_2} = \left(\frac{2}{3}ight)^2$$\frac{48}{A_2} = \frac{4}{9}$By cross-multiplying,we get:$4 	imes A_2 = 48 	imes 9$$A_2 = \frac{432}{4} = 108 \, cm^2$.Therefore,the area of the larger triangle is $108 \, cm^2$.

Corresponding sides of two similar triangles are in the ratio of $2:3$. If the area of the smaller triangle is $48 \, cm^2$,find the area of the larger triangle (in $cm^2$).

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