You can put this solution on YOUR website! The width of a rectangular gate is 2 meters (m) larger than its height. The diagonal brace measures ~(6)m. Find the width and height.
:
Using the pythag. equation: a^2 + b^2 = c^2
:
c = diagonal (6m)
a = height
b = width
:
It says,"The width of a rectangular gate is 2 m larger than its height.".therefore:
b = (a+2)
so we have:
a^2 + (a+2)^2 = 6^2
FOIL
a^2 + (a^2 + 4a + 4) = 36
:
2a^2 + 4a + 4 - 36 = 0
:
2a^2 + 4a - 32 = 0
Simplify,/2
a^2 + 2a - 16 = 0
:
Use the quadratic formula to find a
In this problem a = 1; b = 2; c = -16
:
:
:
Positive solution
a =
a = 3.123 m is the height
then
b = 5.123 m is the width
:
:
Check solution:
3.123^2 + 5.123^2 =
9.754 + 26.245 = 35.999 ~ 36 which is 6^2
