If the diagonal of a square is doubled to mak | vedclass

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

Question

(A) Let the side of the original square be $x 	ext{ cm}$.The diagonal of the original square is $d_1 = \sqrt{2}x 	ext{ cm}$.The area of the original

Vedclass · Accepted Answer

Become $4$-fold

Vedclass · Answer

(A) Let the side of the original square be $x 	ext{ cm}$.The diagonal of the original square is $d_1 = \sqrt{2}x 	ext{ cm}$.The area of the original square is $A_1 = \frac{d_1^2}{2} = \frac{(\sqrt{2}x)^2}{2} = x^2 	ext{ cm}^2$.According to the question,the diagonal of the new square is doubled,so $d_2 = 2 	imes d_1 = 2\sqrt{2}x 	ext{ cm}$.The area of the new square is $A_2 = \frac{d_2^2}{2} = \frac{(2\sqrt{2}x)^2}{2} = \frac{8x^2}{2} = 4x^2 	ext{ cm}^2$.Comparing the areas,$A_2 = 4 	imes A_1$.Therefore,the area of the new square becomes $4$-fold.

If the diagonal of a square is doubled to make another square,the area of the new square will

Similar Questions

The area of a circle is $220 \text{ cm}^2$. The area of a square inscribed in this circle will be (in $\text{cm}^2$):

Three medians $AD, BE$ and $CF$ of $\Delta ABC$ intersect at $G.$ The area of $\Delta ABC$ is $36 \text{ cm}^2$. Then the area of $\Delta CGE$ is (in $\text{cm}^2$)

The ratio of the area of a square to that of the square drawn on its diagonal is

If the ratio of the areas of two squares is $9: 1$,then the ratio of their perimeters is

In the given figure,circle $P$ has a diameter of $2 \ m$ and circle $Q$ has a diameter of $1 \ m$. Find the area of the shaded region.

Vedclass Test Series

Exam Paper Generator

Online Exam Module