In the figure given below,a rectangle of peri | vedclass

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

Question

(C) Let the dimensions of each small congruent rectangle be $x$ and $y$. From the figure,the total width of the large rectangle is $4x$ and also $3y$.

Vedclass · Accepted Answer

$28$

Vedclass · Answer

(C) Let the dimensions of each small congruent rectangle be $x$ and $y$. From the figure,the total width of the large rectangle is $4x$ and also $3y$. Thus,$4x = 3y$,which implies $y = \frac{4}{3}x$. The perimeter of the large rectangle is given by $2 	imes (	ext{length} + 	ext{width}) = 76$. The length of the large rectangle is $4x$ (or $3y$) and the height is $x + y$. So,$2(4x + x + y) = 76$,which simplifies to $5x + y = 38$. Substituting $y = \frac{4}{3}x$ into the equation: $5x + \frac{4}{3}x = 38$. $\frac{15x + 4x}{3} = 38 \implies 19x = 114 \implies x = 6$. Then $y = \frac{4}{3}(6) = 8$. The perimeter of each smaller rectangle is $2(x + y) = 2(6 + 8) = 2(14) = 28 	ext{ units}$.

In the figure given below,a rectangle of perimeter $76$ units is divided into $7$ congruent rectangles. What is the perimeter of each of the smaller rectangles?

Similar Questions

Let $PQR$ be a right-angled isosceles triangle,right-angled at $P(2, 1)$. If the equation of the side $QR$ is $2x + y = 3$,then the equation of one of the sides other than $QR$ is

Points inside the triangle with vertices at $(1,3), (5,0)$ and $(-1,2)$ must necessarily satisfy which of the following conditions?

The area of the triangle formed by the line $x \sin \alpha + y \cos \alpha = \sin 2\alpha$ and the coordinate axes is

If the vertices of a triangle have integer coordinates,then what type of triangle can it never be?

The set of values that $\beta$ can assume so that the point $(0, \beta)$ lies on or inside the triangle formed by the lines $3x+y+2=0$,$2x-3y+5=0$,and $x+4y-14=0$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module