(B) $(1)$ True: In a rhombus, all sides are equal. Perimeter $= 4 \times \text{side} = 4 \times 12 \, \text{cm} = 48 \, \text{cm}$.$(2)$ False: In a s

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(B) $(1)$ True: In a rhombus, all sides are equal. Perimeter $= 4 \times \text{side} = 4 \times 12 \, \text{cm} = 48 \, \text{cm}$.$(2)$ False: In a square $PQRS$, the diagonal $PR = s\sqrt{2}$, where $s$ is the side length. Given $PR = 8 \, \text{cm}$, then $s\sqrt{2} = 8 \implies s = 8 / \sqrt{2} = 4\sqrt{2} \, \text{cm}$. The perimeter is $4s = 4 \times 4\sqrt{2} = 16\sqrt{2} \, \text{cm}$, which is not $32 \, \text{cm}$.

Class 9 Mathematics Quadrilaterals Mix Examples - Quadrilaterals

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State whether each of the following statements is true or false:
$(1)$ $ABCD$ is a rhombus. If $AB = 12 \, \text{cm}$, then the perimeter of $ABCD$ is $48 \, \text{cm}$.
$(2)$ $PQRS$ is a square. If $PR = 8 \, \text{cm}$, then the perimeter of $PQRS$ is $32 \, \text{cm}$.

A
True,True
B
True,False
C
False,True
D
False,False

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Mix Examples - Quadrilaterals

In $\triangle ABC$,$AB = 5\, cm$,$BC = 8\, cm$,and $CA = 7\, cm$. If $D$ and $E$ are respectively the mid-points of $AB$ and $BC$,determine the length of $DE$. (in $, cm$)

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

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In $\Delta PQR$,$A$,$B$,and $C$ are the mid-points of $PQ$,$QR$,and $RP$ respectively. If the perimeter of $\Delta ABC$ is $18.6 \, cm$,then the perimeter of $\Delta PQR$ is $\ldots \ldots \ldots cm$.

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In the figure,$X$ and $Y$ are respectively the mid-points of the opposite sides $AD$ and $BC$ of a parallelogram $ABCD$. Also,$BX$ and $DY$ intersect $AC$ at $P$ and $Q$ respectively. Show that $AP = PQ = QC$.

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In trapezium $ABCD$,$AB \parallel CD$. If $\angle A = 70^{\circ}$ and $\angle B = 85^{\circ}$,then $\angle D = \ldots$ (in $^{\circ}$)

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State whether each of the following statements is true or false:$(1)$ $ABCD$ is a rhombus. If $AB = 12 \, \text{cm}$, then the perimeter of $ABCD$ is $48 \, \text{cm}$.$(2)$ $PQRS$ is a square. If $PR = 8 \, \text{cm}$, then the perimeter of $PQRS$ is $32 \, \text{cm}$.

Similar Questions

In $\triangle ABC$,$AB = 5\, cm$,$BC = 8\, cm$,and $CA = 7\, cm$. If $D$ and $E$ are respectively the mid-points of $AB$ and $BC$,determine the length of $DE$. (in $, cm$)

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

In $\Delta PQR$,$A$,$B$,and $C$ are the mid-points of $PQ$,$QR$,and $RP$ respectively. If the perimeter of $\Delta ABC$ is $18.6 \, cm$,then the perimeter of $\Delta PQR$ is $\ldots \ldots \ldots cm$.

In the figure,$X$ and $Y$ are respectively the mid-points of the opposite sides $AD$ and $BC$ of a parallelogram $ABCD$. Also,$BX$ and $DY$ intersect $AC$ at $P$ and $Q$ respectively. Show that $AP = PQ = QC$.

In trapezium $ABCD$,$AB \parallel CD$. If $\angle A = 70^{\circ}$ and $\angle B = 85^{\circ}$,then $\angle D = \ldots$ (in $^{\circ}$)

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State whether each of the following statements is true or false:
$(1)$ $ABCD$ is a rhombus. If $AB = 12 \, \text{cm}$, then the perimeter of $ABCD$ is $48 \, \text{cm}$.
$(2)$ $PQRS$ is a square. If $PR = 8 \, \text{cm}$, then the perimeter of $PQRS$ is $32 \, \text{cm}$.