SOLUTION: A square mat has a uniform red border on all four sides. The rest of the mat is blue. The width of the blue square is three-fourths the width of the entire square. If the area c

Question 168097This question is from textbook Hall Mercer Intermediate Algebra
: A square mat has a uniform red border on all four sides. The rest of the mat is blue. The width of the blue square is three-fourths the width of the entire square. If the area colored red is 28 m squared, determine the lengths of each side of the mat.
I have tried W^2 - 3/4W^2 = 28
Also W^2 - (W-1/4)^2=28
Mainly need help on setting up. I am alright after the problem is set up into a math problem rather than a word problem.
Thanks This question is from textbook Hall Mercer Intermediate Algebra

Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!

LOOKS TO ME LIKE YOU ARE RIGHT ON WITH THE FIRST TRY!!!!!!
Let W=width of entire square
Then 0.75W=width of the blue square
Area colored red would be width of entire square minus width of blue square, or:
Area colored red=W^2-0.75W^2 and we are told that this equals 28 sq m, so, our equation to solve is:
W^2-0.75W^2=28 or
0.25W^2=28 divide each side by 0.25
W^2=112 sq m take square root of each side
W=plus or minus 10.6 m disregard negative value for W
W=10.6 m
0.75W=0.75*10.6=7.95 m
CK
112-84=28
28=28
Hope this helps----ptaylor
RELATED QUESTIONS
Hey, Please help me solve this problem: A square mat used for athletic exercises... (answered by scott8148)

This one has been answered but the answer does not make sense. I emailed the tutor and... (answered by gonzo,nerdybill,Mathtut)

A square mat has an area of 225 cm2.what is the length of each side of the mat? (answered by nerdybill)

the length of a rectangle mat is 4 m and its breadth is 2.5 m. A 0.1 m wide border is... (answered by TimothyLamb)

A karate match is held on a square mat that has a area 676 ft. squared. What is the... (answered by rapaljer)

Tee-jay has a photo that measures 10cm by 15cm. He want to fix it to a mat, so that there (answered by josgarithmetic)

An 8 in. by 10 in. picture is matted and placed in a frame that will display a total of... (answered by josgarithmetic,josmiceli)

A picture that measures 10cm by 8cm is to be surrounded by a mat before framing. The... (answered by checkley77)

A picture that measures 10 cm by 5 cm is to be surrounded by a mat before being framed.... (answered by mananth)