Two rectangles are shown below. Rectangle P has a perimeter of 20 inches. Rectangle Q has a perimeter of 30 inches. What are the
values of j and h?
1 answer:
The complete question in the attached figure
we know that
perimeter of a rectangle=2*[base+height]
rectangle P
perimeter=20 in
perimeter=2*[j+4+h]
20=2j+2h+8------> 2j+2h=12----> j+h=6-----> j=6-h------> equation 1
rectangle Q
perimeter=30 in
perimeter=2*[j+1+3h]
30=2j+6h+2----> 2j+6h=28----> j+3h=14-------> equation 2
substitute equation 1 in equation 2
(6-h)+3h=14-----> 2h=8-----> h=4
j=6-h-----> j=6-4----> j=2
the answer is
j=2
h=4
we know that
perimeter of a rectangle=2*[base+height]
rectangle P
perimeter=20 in
perimeter=2*[j+4+h]
20=2j+2h+8------> 2j+2h=12----> j+h=6-----> j=6-h------> equation 1
rectangle Q
perimeter=30 in
perimeter=2*[j+1+3h]
30=2j+6h+2----> 2j+6h=28----> j+3h=14-------> equation 2
substitute equation 1 in equation 2
(6-h)+3h=14-----> 2h=8-----> h=4
j=6-h-----> j=6-4----> j=2
the answer is
j=2
h=4
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Answer: h = 2.5 in
Therefore the dimensions of the file holder are 8, h, and (10 - 2h) as shown in the figure.
The volume of the file holder is
V = 8*h*(10 - 2h) = 80h - 16h²
To maximize V, V'(h) = 0.
That is,
80 - 32 h = 0
h = 80/32 = 2.5 in
V''(h) = -32 guarantees that V is maximum because V'' <0.
Maximum V = 80*(2.5) - 16*(2.5)² = 100 in³
Answer: h = 2.5 in