(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

The diameters of two concentric circles are $8\, cm$ and $10\, cm$. The area of the region between them is

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$A$ playground is in the shape of a rectangle. $A$ sum of ₹ $1,000$ was spent to make the ground usable at the rate of $25$ $paisa$ per $m^2$. The breadth of the ground is $50\, m$. If the length of the ground is increased by $20\, m$,what will be the expenditure in rupees at the same rate per $m^2$?

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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?

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$A$ rectangular park is $65\, m$ long and $50\, m$ wide. Two cross paths,each $2\, m$ wide,are to be constructed parallel to the sides. If these paths pass through the centre of the rectangle and the cost of construction is ₹ $17.25$ per $m^2$,then find the total cost involved in the construction (in ₹).

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$A$ can go round a circular path $8$ times in $40$ minutes. If the diameter of the circle is increased to $10$ times the original diameter,then the time required by $A$ to go round the new path once,travelling at the same speed as before,is (in $min$)

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The diameters of two concentric circles are $8\, cm$ and $10\, cm$. The area of the region between them is

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?

$A$ can go round a circular path $8$ times in $40$ minutes. If the diameter of the circle is increased to $10$ times the original diameter,then the time required by $A$ to go round the new path once,travelling at the same speed as before,is (in $min$)

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