The area of a rectangle is A=LW, the area of a square is A=S^2.
W=S-2 and L=2S-3
And we are told that the areas of each figure are the same.
S^2=LW, using L and W found above we have:
S^2=(2S-3)(S-2) perform indicated multiplication on right side
S^2=2S^2-4S-3S+6 combine like terms on right side
S^2=2S^2-7S+6 subtract S^2 from both sides
S^2-7S+6=0 factor:
S^2-S-6S+6=0
S(S-1)-6(S-1)=0
(S-6)(S-1)=0, since W=S-2, and W>0, S>2 so:
S=6 is the only valid value for S. Now we can find the dimensions of the rectangle...
W=S-2 and L=2S-3 given that S=6 in
W=4 in and L=9 in
So the width of the rectangle is 4 inches and the length of the rectangle is 9 inches.
Answers:
11. u = {0, 1/3}
12. n = {-4, 0}
13. s = {-5, 0}
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This is a ratio problem; the ratio of the length to width is constant (and therefore equal):
4 /6 = 15 / x
Now, with a ratio, we may do any allowable algebra operation: cross-multiply, invert both sides, multiply or divide both sides by the same amount, etc.
Let's cross-multiply:
4x = (15)(6)
x = 90/4
x = 22.5 in.
To write a number in scientific notation, you need to write the number as a product of a number from 1 to under 10 multiplied by a integer power of 10.
First, what number from 1 to under 10 can you get out of the digits of 150,000,000 just by changing the decimal point? The answer is 1.5 since 1.5 is greater than or equal to 1 and less than 10.
150,000,000 = 1.5 * 100,000,000
Now we change 100,000,000 into a power of 10. A 1 followed by a number of zeros is the same as 10 to the power equal to the number of zeros. In 100,000,000 the 1 is followed by 8 zeros, so 100,000,000 = 10^8.
150,000,000 = 1.5 * 10^8
Answer:
total surface area = 76 sq.cm
Step-by-step explanation:
total surface area of cuboid = 2 ( lb + lh + bh )
( where l is length , b is width and h is height )
so, surface area :
= 2[ (5×4) + (5×2) + (2×4) ]
= 2 [ 20 + 10 + 8 ]
= 2 × 38
= 76 sq.cm
