The perimeter of rhombus ABCD is 68. If AC = | vedclass

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

Question

(A) rhombus is a quadrilateral where all sides are equal. Let the side length be $s$.Given the perimeter is $68$,we have $4s = 68$,which implies $s =

Vedclass · Accepted Answer

$16$

Vedclass · Answer

(A) rhombus is a quadrilateral where all sides are equal. Let the side length be $s$.Given the perimeter is $68$,we have $4s = 68$,which implies $s = 17$.In a rhombus,the diagonals bisect each other at right angles $(90^{\circ})$.Let the diagonals $AC$ and $BD$ intersect at point $O$.Since $AC = 30$,the length $AO = AC / 2 = 15$.In the right-angled triangle $	riangle AOB$,by the Pythagorean theorem,$AO^2 + BO^2 = AB^2$.Substituting the values: $15^2 + BO^2 = 17^2$.$225 + BO^2 = 289$.$BO^2 = 289 - 225 = 64$.$BO = \sqrt{64} = 8$.Since the diagonals bisect each other,$BD = 2 	imes BO = 2 	imes 8 = 16$.

The perimeter of rhombus $ABCD$ is $68$. If $AC = 30$,find $BD$.

Similar Questions

$\Delta PQR \sim \Delta DEF$ for the correspondence $PQR \leftrightarrow DEF$. If $3 PQ = 2 DE$,$EF = 6$,and $PR = 8$,find $QR$ and $DF$.

Find the value of $x$ for which $DE \parallel AB$ in the given figure.

In $\Delta ABC$, $M$ and $N$ are the midpoints of $\overline{AB}$ and $\overline{AC}$ respectively. If the area of $\Delta ABC$ is $90$, find the area of $\Delta AMN$.

In an isosceles right-angled triangle, the length of the hypotenuse is $20$. Find the perimeter and the area of the triangle.

In $\Delta ABC$,$D$,$E$,and $F$ are the midpoints of $\overline{AB}$,$\overline{BC}$,and $\overline{CA}$ respectively. Then the correspondence $DEF \leftrightarrow \dots$ is a similarity.

Vedclass Test Series

Exam Paper Generator

Online Exam Module