CA Foundation Exam > CA Foundation Questions > Two squares have side p cm and (p+5) cms. The...
Start Learning for Free
Two squares have side p cm and (p+5) cms. The sum of their squares is 625 sq. cm the side of the squares are?
Most Upvoted Answer
Two squares have side p cm and (p+5) cms. The sum of their squares is ...
Problem Statement
Given two squares with sides p cm and (p + 5) cm, the sum of their squares equals 625 sq. cm. We need to find the values of p.
Step 1: Set Up the Equation
The area of the first square is:
- p²
The area of the second square is:
- (p + 5)²
The equation based on the problem statement is:
- p² + (p + 5)² = 625
Step 2: Expand the Equation
Expanding (p + 5)² gives:
- (p + 5)² = p² + 10p + 25
Now, substitute back into the equation:
- p² + (p² + 10p + 25) = 625
This simplifies to:
- 2p² + 10p + 25 = 625
Step 3: Simplify the Equation
Rearranging gives:
- 2p² + 10p + 25 - 625 = 0
- 2p² + 10p - 600 = 0
Dividing the entire equation by 2 results in:
- p² + 5p - 300 = 0
Step 4: Solve the Quadratic Equation
Using the quadratic formula, p = (-b ± √(b² - 4ac)) / 2a:
- Here, a = 1, b = 5, c = -300
Calculating the discriminant:
- b² - 4ac = 5² - 4(1)(-300) = 25 + 1200 = 1225
Thus, the roots are:
- p = (-5 ± 35) / 2
Calculating the two possible values:
- p = (30 / 2) = 15 (positive root)
- p = (-40 / 2) = -20 (not valid as side length cannot be negative)
Step 5: Final Answer
The side lengths of the squares are:
- First square: 15 cm
- Second square: 20 cm (15 + 5)
Given two squares with sides p cm and (p + 5) cm, the sum of their squares equals 625 sq. cm. We need to find the values of p.
Step 1: Set Up the Equation
The area of the first square is:
- p²
The area of the second square is:
- (p + 5)²
The equation based on the problem statement is:
- p² + (p + 5)² = 625
Step 2: Expand the Equation
Expanding (p + 5)² gives:
- (p + 5)² = p² + 10p + 25
Now, substitute back into the equation:
- p² + (p² + 10p + 25) = 625
This simplifies to:
- 2p² + 10p + 25 = 625
Step 3: Simplify the Equation
Rearranging gives:
- 2p² + 10p + 25 - 625 = 0
- 2p² + 10p - 600 = 0
Dividing the entire equation by 2 results in:
- p² + 5p - 300 = 0
Step 4: Solve the Quadratic Equation
Using the quadratic formula, p = (-b ± √(b² - 4ac)) / 2a:
- Here, a = 1, b = 5, c = -300
Calculating the discriminant:
- b² - 4ac = 5² - 4(1)(-300) = 25 + 1200 = 1225
Thus, the roots are:
- p = (-5 ± 35) / 2
Calculating the two possible values:
- p = (30 / 2) = 15 (positive root)
- p = (-40 / 2) = -20 (not valid as side length cannot be negative)
Step 5: Final Answer
The side lengths of the squares are:
- First square: 15 cm
- Second square: 20 cm (15 + 5)
Attention CA Foundation Students!
To make sure you are not studying endlessly, EduRev has designed CA Foundation study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in CA Foundation.
|
Explore Courses for CA Foundation exam
|
|
Top Courses for CA FoundationView all
Two squares have side p cm and (p+5) cms. The sum of their squares is 625 sq. cm the side of the squares are?
Question Description
Two squares have side p cm and (p+5) cms. The sum of their squares is 625 sq. cm the side of the squares are? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about Two squares have side p cm and (p+5) cms. The sum of their squares is 625 sq. cm the side of the squares are? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two squares have side p cm and (p+5) cms. The sum of their squares is 625 sq. cm the side of the squares are?.
Two squares have side p cm and (p+5) cms. The sum of their squares is 625 sq. cm the side of the squares are? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about Two squares have side p cm and (p+5) cms. The sum of their squares is 625 sq. cm the side of the squares are? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two squares have side p cm and (p+5) cms. The sum of their squares is 625 sq. cm the side of the squares are?.
Solutions for Two squares have side p cm and (p+5) cms. The sum of their squares is 625 sq. cm the side of the squares are? in English & in Hindi are available as part of our courses for CA Foundation.
Download more important topics, notes, lectures and mock test series for CA Foundation Exam by signing up for free.
Here you can find the meaning of Two squares have side p cm and (p+5) cms. The sum of their squares is 625 sq. cm the side of the squares are? defined & explained in the simplest way possible. Besides giving the explanation of
Two squares have side p cm and (p+5) cms. The sum of their squares is 625 sq. cm the side of the squares are?, a detailed solution for Two squares have side p cm and (p+5) cms. The sum of their squares is 625 sq. cm the side of the squares are? has been provided alongside types of Two squares have side p cm and (p+5) cms. The sum of their squares is 625 sq. cm the side of the squares are? theory, EduRev gives you an
ample number of questions to practice Two squares have side p cm and (p+5) cms. The sum of their squares is 625 sq. cm the side of the squares are? tests, examples and also practice CA Foundation tests.
|
|
Explore Courses for CA Foundation exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup