L = length
W = width
d =diagonal
d = √ ( W² + L²)
W = L - 4
d = √ [ ( L - 4 )² + L²]
d = L + 4
L + 4 = √ [ ( L - 4 )² + L²]
Raise both sides to the power of two.
( L + 4 )² = ( L - 4 )² + L²
L²+ 2 L ∙ 4 + 4² = L² - 2 L ∙ 4 + 4² + L²
L²+ 8 L + 16 = L² - 8 L + 16 + L²
Subtract L² + 16 to both sides
8 L = - 8 L + L²
Add 8 L to both sides
8 L + 8 L = - 8 L + L² + 8 L
16 L = L²
Divide both sides by L
16 = L
L = 16 in
W = L - 4 = 16 - 4 = 12
Proof:
d = √ ( W² + L²) = √ ( 16² + 12²) =
√ ( 256 + 144 ) = √ 400 = 20 in
d = L + 4 = 16 + 4
Suppose you want to build a rectangular picture frame where the width is 4 inches less than the length and the diagonal is 4
inches longer than the length. What are the dimensions of the picture frame?
1 answer
1 answer