Domain: ML Topic: Algebraic
Expressions and
Identities
Class: VIII
Expected
Time:10min
Description of item: Three women Rita ,Tara and
Sneha owned a plot each in their village. Rita and
Tara owned square pieces of land and Sneha a
rectangular one. Rita observed the following while
farming-
a) Tara’s plot was 5 m longer than hers
b) Sneha’s plot was 3 m longer on one side and
2m longer on the other side as compared to
her plot.
Learning Outcomes:
(As per NCERT)
Solves puzzles and daily life problems
using variables and multiplies
algebraic expressions.
Uses various algebraic identities in
solving problems of daily life.
Q 1. The dimensions of the three plots of land are tabulated algebraically. See the table and arrange
them in proper order as per the above information .
RITA ( + 3) ( + 2)
TARA ,
SNEHA ( + 5), ( + 5)
Answers
Given : Three women Rita ,Tara and Sneha owned a plot each in their village
Tara’s plot was 5 m longer than Rita plot
Sneha’s plot was 3 m longer on one side and 2m longer on the other side as compared to Rita plot
To Find : whose land has more area
If area of Rita’s land is 400 sq.m , then calculate the land areas of Tara and Sneha.
Solution:
Let sat Rita Land = x * x
Rita Land area = x² m²
perimeter = 4x
Tara’s plot was 5 m longer than hers
Tara Land area = (x + 5)²
= x² + 10x + 25
Perimeter = 4(x + 5) = 4x + 20
Sneha’s plot was 3 m longer on one side and 2m longer on the other side
Sneha Land area = (x + 3)(x + 2)
= x² + 5x + 6
Perimeter = 2(x + 3 + x + 2) = 4x + 10
x² + 10x + 25 > x² + 5x + 6 > x²
Tara > Sneha > Rita
Tara land has maximum area
Tara’s land area will always be greater than Sneha’s land area
area of Rita’s land is 400 sq.m => x² = 400 = > x = 20 m
Tara Land area = (20 + 5)² = 625 m²
Sneha Land area = (20 + 3)(20 + 2) = 506 m²
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