SOLUTION: A small square is cut out of a larger square.
The side lengths of both squares, in centimetres, are whole numbers less than 25. The remaining area of the larger square is 57 squar
Algebra.Com
Question 1011123: A small square is cut out of a larger square.
The side lengths of both squares, in centimetres, are whole numbers less than 25. The remaining area of the larger square is 57 square cm.
What is the perimeter of the small square in centimetres?
Solution: 32 cm
Can you show the work please. Thank you!
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
= side length of the smaller square, in cm,
= side length of the larger square, in cm,
and , of course.
So,
= area of the smaller square, in square cm;
= original area of the larger square, in square cm, and
= remaining area of the larger square, in square cm.
The problem tells us that ,
and that and are positive integers less than 25.
Algebra tells us that
<--> .
Since and are positive integers less than , with and are positive integers, and
.
What positive integers less than could be and ?
As does not have too many factors, we can only write it as two products of positive integers:
and .
Only one of thpose products has both factors less than .
So, ----> .
The perimeter of the small square in centimetres is
.
RELATED QUESTIONS
A piece of wire 64 centimeters in length is cut into two parts. Each part is then bent to (answered by palanisamy)
The length of each side of a square is 3in more than the length of each side of a smaller (answered by scott8148)
A piece of wire 64 centimeters in length is cut into two parts. Each part is then bent to (answered by ankor@dixie-net.com)
A piece of twine 48 inches long is cut into two lengths. Each length is then used to form (answered by ptaylor)
Mr Black is eccentric but rich. He wanted a piece of land. He asked the estate agent to... (answered by ankor@dixie-net.com)
The side of one square is 3 cm longer than the side of another square. If the sum of the... (answered by MathTherapy)
The side of one square is 3 cm longer than the side of a second square. If the combined... (answered by John10)
The side of one square is 3 cm longer than the side of a second square. If the combined... (answered by ankor@dixie-net.com)
The perimeter of the small square is one third the perimeter of the large square. What... (answered by TimothyLamb)