need help with a word problem

User Generated

avxxv_xnar17

Mathematics

Question Description

We are interested in the dimensions of a certain square. A rectangle has length triple the side of this square and width two units less than the side of this square. If the two areas are equal, what are the square's dimensions (w x h)

Student has agreed that all tutoring, explanations, and answers provided by the tutor will be used to help in the learning process and in accordance with Studypool's honor code & terms of service.

Explanation & Answer

Thank you for the opportunity to help you with your question!

let the side of the square be s, then the rectangle has length 3s and width s-2.

the area of square is s*s=s^2 and that of the rectangle is 3s(s-2)=(3s^2-6s).

the areas are equal, therefore 3s^2-6s=s^2

3s^2-s^2-6s=0

2s^2-6s=0

2s(s-3)=0, s=0 or s=3.

then the squares dimension is 3 by 3. Hence the area of square is 9 square units

Please let me know if you need any clarification. I'm always happy to answer your questions.

ZnguUryc01 (10)
UC Berkeley

Anonymous
This is great! Exactly what I wanted.

Studypool
4.7
Trustpilot
4.5
Sitejabber
4.4