Fifth grade
ee. 12 area and perimeter: word problems
a rectangular sticker has an area of 10 square centimeters and a perimeter of 14
centimeters. what are the dimensions of the sticker?

Length = 5 cm, width = 2 cm.

Step-by-step explanation:

If L is the length and W the width we have the equations:

LW = 10            <  The area.

2L + 2W = 14      < The perimeter.

From the first equation L = 10/W so substituting for L in the second equation:

2 * 10/W + 2W = 14

20/W + 2W = 14             Multiplying through by W:

20 + 2W^2 = 14W

2W^2 - 14W + 20 = 0      Dividing by 2:

W^2 - 7W + 10 = 0  

(W - 5)(W - 2) = 0

W = 5 or 2.

So W is either  2 or 5 cm.

Substituting W = 2 in LW = 10

L * 2 = 10

L = 5 cm.

The length is longer than the width so the length is 5 cm and the width = 2 cm.

v = 1/3 a^2h

step-by-step explanation:

if the height is 57.7cm and the height of the slant edge is 18.2cm, then the volume is 1/3 a^2h.

answer: c, the green line

step-by-step explanation:

there is no black line, eliminate b.

simple interest implies periodic payments, but the red line shows no payments, eliminate d.

simple interest has equal payments. if paid say every day, the graph is about a straight line (actually a stairstep).

the yellow line is not straight, eliminate a.

check: the green line is straight, answer is c.

simple interest with positive interest rate gives a straight line sloping up to the right. green line:

g(t) = $100 + ($200-$100) ÷ (20 years) × (t years)

= $100 + (4%/year) × ($100)(t years)

incidentally, the yellow line curving upward represents continuously compounded interest

y = $100 × 2^(t years / (14 assuming the yellow line hits $200 at 14 years. 2^0 is 1, so y(0) = $100; 2^(14/14) is 2, so y(14) = $200.