If each side of a triangle is doubled,then fi | vedclass

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

Question

(B) Let $a, b, c$ be the sides of the given triangle and $s$ be its semi-perimeter.Then,$s = \frac{a+b+c}{2}$,which implies $2s = a+b+c$ $...(1)$.The

Vedclass · Accepted Answer

$4:1$

Vedclass · Answer

(B) Let $a, b, c$ be the sides of the given triangle and $s$ be its semi-perimeter.Then,$s = \frac{a+b+c}{2}$,which implies $2s = a+b+c$ $...(1)$.The area of the given triangle is $\Delta = \sqrt{s(s-a)(s-b)(s-c)}$.According to the problem,the sides of the new triangle are $2a, 2b$,and $2c$.Let $S$ be the semi-perimeter of the new triangle.$S = \frac{2a+2b+2c}{2} = a+b+c = 2s$ $...(2)$.The area of the new triangle is $\Delta' = \sqrt{S(S-2a)(S-2b)(S-2c)}$.Substituting $S = 2s$ into the formula:$\Delta' = \sqrt{2s(2s-2a)(2s-2b)(2s-2c)}$$\Delta' = \sqrt{2s \cdot 2(s-a) \cdot 2(s-b) \cdot 2(s-c)}$$\Delta' = \sqrt{16s(s-a)(s-b)(s-c)}$$\Delta' = 4\sqrt{s(s-a)(s-b)(s-c)} = 4\Delta$.Thus,the ratio of the area of the new triangle to the given triangle is $\frac{\Delta'}{\Delta} = \frac{4\Delta}{\Delta} = 4:1$.

If each side of a triangle is doubled,then find the ratio of the area of the new triangle thus formed to the area of the given triangle.

Similar Questions

In $\Delta ABC$,$AB = 20 \, cm$,$BC = 48 \, cm$,and $AC = 52 \, cm$,find the area of $\Delta ABC$. (in $, cm^2$)

Find the area of the parallelogram given in the figure. Also,find the length of the altitude from vertex $A$ on the side $DC.$

From a point in the interior of an equilateral triangle,perpendiculars are drawn on the three sides. The lengths of the perpendiculars are $14 \, cm$,$10 \, cm$,and $6 \, cm$. Find the area of the triangle.

$A$ design is made on a rectangular tile of dimensions $50\, cm \times 70\, cm$ as shown in the figure. The design shows $8$ triangles,each with sides $26\, cm, 17\, cm$,and $25\, cm$. Find the total area of the design and the remaining area of the tile.

In Heron's formula,$s$ represents ............

Vedclass Test Series

Exam Paper Generator

Online Exam Module