SOLUTION: A single piece of rectangular cardboard can be folded around a 5” by 7” photo and taped along the seams to create a protective cover suitable for mailing. If the cardboard is folde
Algebra ->
Angles
-> SOLUTION: A single piece of rectangular cardboard can be folded around a 5” by 7” photo and taped along the seams to create a protective cover suitable for mailing. If the cardboard is folde
Log On
Question 935727: A single piece of rectangular cardboard can be folded around a 5” by 7” photo and taped along the seams to create a protective cover suitable for mailing. If the cardboard is folded as shown with no gap or overlap, find the dimensions of the original cardboard. Round to the nearest hundredth. (HINT: Use Theorem 6.9 states: In a right triangle, the altitude to the hypotenuse is the mean proportional between the two segments formed by the altitude on the hypotenuse.)
Answer by TimothyLamb(4379) (Show Source):
You can put this solution on YOUR website! A = small right triangle with 5" hypotenuse
B = large right triangle with 7" hypotenuse
---
x = short side of A:
y = long side of A:
z = short side of B:
w = long side of B:
---
triangles A and B together form a third triangle similar to A and similar to B, but larger than A, lets call this third triangle C
---
u = hypotenuse of C:
u = sqrt( 5*5 + 7*7 )
u = 8.60232526704
---
use the proportionality of similar triangles A and C:
(short side of A)/(hypotenuse of A) = (short side of C)/(hypotenuse of C)
x/5 = 5/u
x/5 = 5/u
x = 5*5/u
x = 5*5/8.60232526704
x = 2.9061909686
---
use the proportionality of similar triangles A and C:
(long side of A)/(hypotenuse of A) = (long side of C)/(hypotenuse of C)
y/5 = 7/u
y = 5*7/u
y = 5*7/8.60232526704
y = 4.06866735603
---
use the proportionality of similar triangles B and C:
(short side of B)/(hypotenuse of B) = (short side of C)/(hypotenuse of C)
z/7 = 5/u
z = 7*5/u
z = 7*5/8.60232526704
z = 4.06866735603
---
use the proportionality of similar triangles B and C:
(long side of B)/(hypotenuse of B) = (long side of C)/(hypotenuse of C)
w/7 = 7/u
w = 7*7/u
w = 7*7/8.60232526704
w = 5.69613429845
---
the folding corners of the cardboard are just similar copies of triangles A and B:
---
dimensions of the cardboard:
---
length of top-left edge = length of bottom-right edge = y + z
y + z = 4.06866735603 + 4.06866735603
y + z = 8.13733471206
---
length of top-right edge = length of bottom-left edge = x + w
x + w = 2.9061909686 + 5.69613429845
x + w = 8.60232526705
---
answer:
L = 8.60 inches
W = 8.14 inches
---
Free algebra tutoring live chat:
https://sooeet.com/chat.php?gn=algebra
---
Solve and graph linear equations:
https://sooeet.com/math/linear-equation-solver.php
---
Solve quadratic equations with quadratic formula:
https://sooeet.com/math/quadratic-formula-solver.php
---
Solve systems of linear equations up to 6-equations 6-variables:
https://sooeet.com/math/system-of-linear-equations-solver.php
---
