The areas of two similar triangles are 144 an | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) According to the theorem of areas of similar triangles,the ratio of the areas of two similar triangles is equal to the square of the ratio of thei

Vedclass · Accepted Answer

$27$

Vedclass · Answer

(B) According to the theorem of areas of similar triangles,the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.Let the areas of the two triangles be $A_1 = 144$ and $A_2 = 81$.Let the corresponding longest sides be $s_1 = 36$ and $s_2 = x$.According to the theorem: $\frac{A_1}{A_2} = (\frac{s_1}{s_2})^2$.Substituting the values: $\frac{144}{81} = (\frac{36}{x})^2$.Taking the square root on both sides: $\sqrt{\frac{144}{81}} = \frac{36}{x}$.This simplifies to: $\frac{12}{9} = \frac{36}{x}$.Further simplifying the fraction: $\frac{4}{3} = \frac{36}{x}$.Cross-multiplying gives: $4x = 36 	imes 3$.$4x = 108$.$x = \frac{108}{4} = 27$.Therefore,the length of the longest side of the second triangle is $27$.

The areas of two similar triangles are $144$ and $81$. If the length of the longest side of the first triangle is $36$,the length of the longest side of the second triangle is........

Similar Questions

$\Delta DEF \sim \Delta PQR$ for the correspondence $DEF \leftrightarrow QPR$. If $2 DE = 3 PQ$ and $QR = 8$,then $DF = \ldots$

Sides of two similar triangles are in the ratio $4:9$. Areas of these triangles are in the ratio

In the figure,$D$ is a point on the hypotenuse $AC$ of $\Delta ABC,$ such that $BD \perp AC,$ $DM \perp BC,$ and $DN \perp AB.$ Prove that $DN^{2} = DM \cdot AN.$

In the figure,if $\angle A = \angle C$,$AB = 6 \, cm$,$BP = 15 \, cm$,$AP = 12 \, cm$,and $CP = 4 \, cm$,then find the lengths of $PD$ and $CD$ (in $cm$).

$E$ is a point on the side $AD$ produced of a parallelogram $ABCD$ and $BE$ intersects $CD$ at $F.$ Show that $\Delta ABE \sim \Delta CFB$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module