(D) Let the length of the rectangle be $l$ and the width be $w$.Diagonal $d = \sqrt{l^2 + w^2}$.Distance covered by $A$ diagonally $= \frac{52 \text{

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(D) Let the length of the rectangle be $l$ and the width be $w$.Diagonal $d = \sqrt{l^2 + w^2}$.Distance covered by $A$ diagonally $= \frac{52 \text{ m}}{60 \text{ s}} \times 15 \text{ s} = 13 \text{ m}$.So,$l^2 + w^2 = 13^2 = 169$.Distance covered by $B$ along the sides $= l + w = \frac{68 \text{ m}}{60 \text{ s}} \times 15 \text{ s} = 17 \text{ m}$.We know that $(l + w)^2 = l^2 + w^2 + 2lw$.Substituting the values: $17^2 = 169 + 2lw$.$289 = 169 + 2lw$.$2lw = 289 - 169 = 120$.Area of the field $= l \times w = \frac{120}{2} = 60 \text{ m}^2$.

Competitive Quantitative Aptitude Mensuration Measurement of Area

Medium

$A$ person $A$ takes $15 \text{ seconds}$ to cross a rectangular field diagonally walking at a speed of $52 \text{ m/min}$. $A$ person $B$ takes the same time to cross the same field along its sides (length + width) walking at a speed of $68 \text{ m/min}$. The area of the field is $....... \text{ m}^2$.

A
$30$
B
$40$
C
$50$
D
$60$

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Mensuration

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Measurement of Area

In the given figure,the radius of the circle is $14 \sqrt{2} \text{ cm}$. $PQRS$ is a square. $EFGH$,$ABCD$,$WXYZ$,and $LMNO$ are four identical squares. What is the total area (in $\text{cm}^2$) of all the small squares?

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The ratio of the $3$ angles of a quadrilateral is $13: 9: 5$. The value of the $4^{th}$ angle of the quadrilateral is $36^{\circ}$. What is the difference between the largest and the second smallest angles of the quadrilateral? (in $^{\circ}$)

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$A$ sphere of $30 \ cm$ radius is dropped into a cylindrical vessel of $80 \ cm$ diameter,which is partly filled with water. If its level rises by $x \ cm$,find $x$ (in $cm$). (in $.5$)

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$ABCD$ is a parallelogram in which diagonals $AC$ and $BD$ intersect at $O$. If $E, F, G$ and $H$ are the midpoints of $AO, DO, CO$ and $BO$ respectively,then the ratio of the perimeter of the quadrilateral $EFGH$ to the perimeter of parallelogram $ABCD$ is

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If the area of a square increases by $69 \%$,then the side of the square increases by (in $\%$)

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In the given figure,the radius of the circle is $14 \sqrt{2} \text{ cm}$. $PQRS$ is a square. $EFGH$,$ABCD$,$WXYZ$,and $LMNO$ are four identical squares. What is the total area (in $\text{cm}^2$) of all the small squares?

The ratio of the $3$ angles of a quadrilateral is $13: 9: 5$. The value of the $4^{th}$ angle of the quadrilateral is $36^{\circ}$. What is the difference between the largest and the second smallest angles of the quadrilateral? (in $^{\circ}$)

$A$ sphere of $30 \ cm$ radius is dropped into a cylindrical vessel of $80 \ cm$ diameter,which is partly filled with water. If its level rises by $x \ cm$,find $x$ (in $cm$). (in $.5$)

$ABCD$ is a parallelogram in which diagonals $AC$ and $BD$ intersect at $O$. If $E, F, G$ and $H$ are the midpoints of $AO, DO, CO$ and $BO$ respectively,then the ratio of the perimeter of the quadrilateral $EFGH$ to the perimeter of parallelogram $ABCD$ is

If the area of a square increases by $69 \%$,then the side of the square increases by (in $\%$)

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