Two cross roads, each of width 5 m , run at right angles through … - Vidyadip

Question

Two cross roads, each of width 5 m , run at right angles through the centre of a rectangular park of length 70 m and breadth 45 m parallel to its sides. Find the area of the roads. Also, find the cost of constructing the roads at the rate of Rs. 105 per $m ^2$.

✓

Answer

Let $A B C D$ be the rectangular park then $E F G H$ and $I J K L$ the two rectangular roads with width 5 m .

Length of the rectangular park $A D=70 cm$

Breadth of the rectangular park $C D=45 m$

Area of the rectangular park $=$ Length $\times$ Breadth $=70 m \times 45 m=3150 m^2$

Area of the road $EFGH =70 m \times 5 m=350 m^2$

Area of the road JKIL $=45 m \times 5 m=225 m^2$

Clearly area of MNOP is common to the two roads.

Thus, Area of MNOP $=5 m \times 5 m=25 m^2$

Hence,

Area of the roads $=$ Area $(E F G H)+$ Area(JKIL) - Area(MNOP $)$

$=(350+225) m^2-25 m^2=550 m^2$

Again, it is given that the cost of constructing the roads $=$ Rs. 105 per $m ^2$

Therefore,

Cost of constructing $550 m^2$ area of the roads $=$ Rs. $(105 \times 550)$

= Rs. 57750

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "5 Mark Question" from Mensuration - I (Perimeter and Area of Rectilinear Figures)→Mensuration - I (Perimeter and Area of Rectilinear Figures) — all question types→Maths STD 7 question papers→Maharashtra Board STD 7 question papers→Maharashtra Board question paper generator→

Similar questions

Virat and Samrat together invested Rs 50000 and Rs 120000 to start a business. They suffered a loss of 20%. How much loss did each of them incur ?

Look at the bar graph given below.

Read it care fully and answer the following questions.

What information does the bar graph give?
In which subject is the student very good?
In which subject is the poor?
What is the average of his marks?

Draw $\triangle\text{DEF}$ such that DE= DF= 4cm and EF = 6cm. Measure $\angle\text{E}$ and $\angle\text{F}.$

Find the value of p, if the mean of the following distribution is 20

x:	15	17	19	20 + p	23
f:	2	3	4	5 p	6

Can you give examples from science or everyday life of quantities that vary in direct proportion ?

Draw any $\triangle\text{ABC}.$ Bisect side AB at D. Through D, draw a line parallel to BC, meeting AC in E. Measure AE and EC.

In the given figure. DE || BC. If $\angle\text{C}=65^\circ$ and $\angle\text{B}=55^\circ$, find

$\angle\text{ADE}$
$\angle\text{AED}$
$\angle\text{C}$

Number of children in six different classes are given below. Represent the data on a bar graph.

Class	V	VI	VII	VIII	IX	X
Number of children	135	120	95	100	90	80

Which class has the maximum number of children?
Which class has the minimum number of children?

How do you choose the scale?

Draw triangle with the measures given. In ∆ABC, l(AC) = 7.5 cm, m∠ABC = 90°, l(BC) = 5.5cm.

Draw a $\triangle\text{ABC}$ with AB = 6cm, BC = 7cm and CA = 8cm. Using ruler and compass alone, draw (i) the bisector AD of $\angle\text{A}$ and (ii) perpendicular AL from A on BC. Measure LAD.