Question

for a scale factor less than 2 the ratio of the area of triangle to be constructed and the triangle given will be always
a) 2
b) less than 2
c) less than 4
d) greater than 4​

Answer 1

c......................

answer for aakash test....

Answer 2

The ratio of the area of triangle to be constructed (ΔKLM) to the area of triangle given (ΔUVW) is lesser than 4 and option (c) is correct

Step-by-step explanation:

Given:

For a scale factor less than 2 the ratio of the area of triangle to be constructed to the area of triangle. 

To Find:

The ratio of the area of triangle to be constructed  to the area of triangle.

Solution:

Let the scale factor be p : q.

Then,   $\frac{p}{q} < 2$

$p < 2q$ ------------- equation no.01.

Let the triangle to be constructed be ΔKLM and the given triangle  ΔUVW.

As ΔKLM∼ΔUVW

Δ KLM is a triangle whose sides are p and q  of the corresponding sides of ΔUVW.

Thus,$\frac{KL}{UV} =\frac{LM}{VW} =\frac{MK}{WU} =\frac{p}{q}$   -------equation no.02

(Ratio of corresponding sides of similar triangles are equal).$\frac{Area\ of\ (\triangle KLM)}{Area\ of(\triangle UVW)} =(\frac{KL}{UV} )^{2}$  (Ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.)

$\frac{Area\ of\ (\triangle KLM)}{Area\ of(\triangle UVW)} =(\frac{p}{q} )^{2}$ --------------------- equation no.03.

$p < 2q$      -------- Form  equation no.01.

Squaring both sides, we get.

$p^{2} < (2q)^{2}$

$p^{2} < 4q^{2}$

$\frac{p^{2} }{q^{2} } < 4$

Putting value of $\frac{p^{2} }{q^{2} }$  in equation 03.

$\frac{Area\ of\ (\triangle KLM)}{Area\ of(\triangle UVW)} < 4$

Thus, the ratio of the area of triangle to be constructed (ΔKLM) to the area of triangle given (ΔUVW) is lesser than 4 and option (c) is correct.

PROJECT CODE #SPJ3