In Text Questions Try These (Text Book Page No.50, 52,58,60,63,65) - Chapter 3 Algebra Term 3 7th Maths Guide Samacheer Kalvi Solutions - SaraNextGen [2024-2025]

Updated By SaraNextGen

On April 24, 2024, 11:35 AM

Text Questions :  Chapter 3 Algebra Term 3 Class 7th std Maths Guide Samacheer Kalvi Solutions
Exercise $3.1$
Think (Text book Page No. 50)
Question 1.
Is it the only way to decompose the numbers representing length and breadth? Discuss.
Solution:
No, for example 15 can be decompose into $1 \times 15,3 \times 5,5 \times 3,15 \times 1$

Try These (Text book Page No. 52)
Question 1.
Observe the following figures and try to find its area, geometrically. Also verify the same by multiplication of monomial.

Area of each box $=\mathrm{xy}$
Totally 12 boxes
$\therefore$ Total area $=12 \times x y=12 x y$
Also multiplying the length $4 x$ and breadth $3 y$
We have area of the rectangle $=4 x \times 3 y=12 x y$
(ii) Area of each small box $=\mathrm{x}^{2}$
Total number of boxes $=3$
$\therefore$ Total area $=3 \mathrm{x}^{2}$
Also length of the rectangle $=3 x$
breadth of the rectangle $=\mathrm{x}$
Area of the rectangle $=$ length $\times$ breadth
$=3 x \times x$
$=3 x^{2}$
(iii) Area of each small box is ay, by, cy
$\therefore$ Total area $=a y+b y+c y=y(a+b+c)$
Area of the rectangle $=$ length $\times$ breadth
$=(a+b+c) y$
(iv) Area of each small square $=x^{2}$
There are 4 small squares
$\therefore$ Total area of the given square $=4 \mathrm{x}^{2}$
Also side of the big square $=2 x$
$\therefore$ Area of the square $=(2 x)^{2}=4 x^{2}$
(v) Area of each $s m a l l$ rectangle $=x y$
There are 9 such rectangles
$\therefore$ Total area $=9 x y$
Area of big rectangle $=$ lenght $\times$ breath
$=3 x \times 3 y=9 x y$
 

Question $2 .$
Let the length and breadth of a tile be $x$ and $y$ respectively. Using such tiles construct as many rectangles as you can and find out the length and breadth of the rectangles so formed such that its area is
(i) $12 \mathrm{xy}$
(ii) $8 x y$
(iii) $9 x y$
Solution:

Try These (Text book Page No. 58)
Question 1.
Consider a square shaped paddy field with side of $48 \mathrm{~m}$. A pathway with uniform breadth is surrounded the square field and the length of the outer side is $52 \mathrm{~m}$. Can you find the area of the pathway by using identities?
Solution:
Let $\mathrm{a}=52$
$b=4$
$(a-b)^{2}=a^{2}-2 a b+$
$\begin{aligned}
&(a-b)^{2}=a^{2}-2 a b+b^{2}=52^{2}-2(52)(4)+4^{2} \\
&=2704-416+16=2304
\end{aligned}$

Think (Text book Page No. 60)
Question $1 .$
Can we factorize the following expressions using any basic identities? Justify your answer.
(i) $x^{2}+5 x+4$
(ii) $x^{2}-5 x+4$

Solution:
(i) $x^{2}+5 x+4=x 2+(1+4) x+(1 \times 4)$
Which is of the form $x^{2}+(a+b) x+a b$
$=(x+a)(x+b)$ $x^{2}+(1+4) x+(1 \times 4)=(x+1)(x+4)$ $\therefore x^{2}+5 x+4=(x+1)(x+4)$
$\begin{aligned}
&x^{2}+(1+4) x+(1 \times 4)=(x+1)(x+4) \\
&\therefore x^{2}+5 x+4=(x+1)(x+4)
\end{aligned}$
(ii) $x^{2}-5 x+4=x^{2}+((-1)+(-4)) x+(-1)(-4)$
Which is of the form $x^{2}+(a+b) x+a b$
$=(x+a)(x+b)$
$\left.x^{2}+((-1)+4)\right) x+((-1)(-4))=(x+(-4))=(x-1)(x-4)$
$\left.x^{2}+((-1)+4)\right) x+((-1)(-4))=(x+(-4))=(x-1)(x-4)$ $\left.x^{2}-5 x+4=(x-1)(x-4)\right)$
 

Exercise $3.2$
Try These (Text book Page No. 63)
Question 1.
Construct inequations for the following statements:
1. Ramesh's salary is more than $₹ 25,000$ per month.
2. This lift can carry maximum of 5 persons.
3. The exhibition will be there in town for at least 100 days.
Solution:
1. $x>25,000$, where $x$ is Ramesh's Salary per month.
2. $y \leq 5$, where $y$ is the maximum number of persons the left can carry.
3. $z \geq 100$, where $z$ is the number of days when the exhibition is there.
 

Think (Text book Page No. 65)
Question 1.
Hameed saw a stranger in the street. He told his parent, "The stranger's age is between 40 to 45 years, and his height is between 160 to $170 \mathrm{~cm}$ "
Convert the above verbal statement into algebraic inequations by using $x$ and $y$ as variables of age and height.
Solution:
Let $x$ be the age and $y$ be the height then
$40 \leq \mathrm{x} \leq 45$ and $160 \leq \mathrm{y} \leq 170$