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2 years ago

16. What are the values of a and b?

Mathematics

1 answer:

MrMuchimi2 years ago

4 0

Answer:

a = 20; b = 2√101

Step-by-step explanation:

The triangle at upper left and the one at lower right are similar. Ratios of corresponding sides are equal, so ...

200/a = a/2

400 = a^2

√400 = 20 = a

Then, by the Pythagorean theorem, the value of b can be found:

b = √(a^2 + 2^2) = √(400 +4) = √4·√101

b = 2√101

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A rectangle with a length of L and a width of W has a diagonal of 10 inches. Express the perimeter P of the rectangle as a funct

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<h2>Answer:</h2>

The expression which represents the perimeter P of the rectangle as a function of L is:

$Perimeter=2(L+\sqrt{100-L^2})$

<h2>Step-by-step explanation:</h2>

The length and width of a rectangle are denoted by L and W respectively.

Also the diagonal of a rectangle is: 10 inches.

We know that the diagonal of a rectangle in terms of L and W are given by:

$10=\sqrt{L^2+W^2}$

( Since, the diagonal of a rectangle act as a hypotenuse of the right angled triangle and we use the Pythagorean Theorem )

Hence, we have:

$10^2=L^2+W^2\\\\i.e.\\\\W^2=100-L^2\\\\W=\pm \sqrt{100-L^2}$

But we know that width can't be negative. It has to be greater than 0.

Hence, we have:

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3 years ago

The rectangle shown has a perimeter of 48 cm and the given area. Its length is 6 more than twice its width. Write and solve a sy

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Answer:

The length of the rectangle is 18 cm

The width of the rectangle is 6 cm

Step-by-step explanation:

Let

x-----> the length of the rectangle

y----> the width of the rectangle

we know that

The perimeter of the rectangle is

$P=2(x+y)$

we have

$P=48\ cm$

$48=2(x+y)$ ------> equation A

$x=2y+6$ ------> equation B

Substitute equation B in equation A and solve for y

48=2(2y+6+y)

48=2(3y+6)

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