The perimeter of a rhombus is 100,cm and one | vedclass

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

Question

(D) Let the side of the rhombus be $a$. Since the perimeter is $100\,cm$,we have $4a = 100\,cm$,which gives $a = 25\,cm$.Let the diagonals of the rhom

Vedclass · Accepted Answer

$14$

Vedclass · Answer

(D) Let the side of the rhombus be $a$. Since the perimeter is $100\,cm$,we have $4a = 100\,cm$,which gives $a = 25\,cm$.Let the diagonals of the rhombus be $d_1 = 48\,cm$ and $d_2$. The diagonals of a rhombus bisect each other at right angles.This forms a right-angled triangle with the side of the rhombus as the hypotenuse and half of the diagonals as the other two sides.Using the Pythagorean theorem: $(a)^2 = (d_1/2)^2 + (d_2/2)^2$.Substituting the values: $(25)^2 = (48/2)^2 + (d_2/2)^2$.$625 = (24)^2 + (d_2/2)^2$.$625 = 576 + (d_2/2)^2$.$(d_2/2)^2 = 625 - 576 = 49$.$d_2/2 = \sqrt{49} = 7$.Therefore,$d_2 = 7 	imes 2 = 14\,cm$.

The perimeter of a rhombus is $100\,cm$ and one of its diagonals measures $48\,cm$. Then,the length of the other diagonal is ....... $cm.$

Similar Questions

Can the angles $110^{\circ}, 80^{\circ}, 70^{\circ}$ and $95^{\circ}$ be the angles of a quadrilateral? Why or why not?

The angles of a quadrilateral are in the ratio $3:4:6:5$. Find the measure of the greatest angle. (in $^\circ$)

In quadrilateral $ABCD$,$\angle A = 100^{\circ}$,$\angle B = 80^{\circ}$,and $\angle C = 120^{\circ}$. Find $\angle D$. (in $^{\circ}$)

$P$ and $Q$ are points on opposite sides $AD$ and $BC$ of a parallelogram $ABCD$ such that $PQ$ passes through the point of intersection $O$ of its diagonals $AC$ and $BD$. Show that $PQ$ is bisected at $O$.

For any convex quadrilateral $ABCD$,prove that $AB + BC + CD + DA < 2(AC + BD)$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module