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

Prove that the area of the equilateral triangle drawn on the hypotenuse of a right-angled triangle is equal to the sum of the areas of the equilateral triangles drawn on the other two sides of the triangle.

In the figure,$ABC$ is a triangle right-angled at $B$ and $BD \perp AC$. If $AD = 4 \, cm$ and $CD = 5 \, cm$,find $BD$ and $AB$.

In $\Delta ABC$,$\overline{AD}$ is a median. If $AB = 8$,$AC = 15$ and $AD = 8.5$,find $BC$.

In $\Delta ABC,$ the midpoints of the sides are $P, Q, R.$ In $\Delta PQR,$ the midpoints of the sides are $X, Y, Z.$ If the area of $\Delta XYZ$ is $20,$ find the area of $\Delta PQR$ and $\Delta ABC.$

In $\Delta ABC$,$m \angle B = 90^{\circ}$ and $AC = 14\sqrt{2}$. If $AB = BC$,find the area of $\Delta ABC$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module