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sergeinik [125]
3 years ago
14

The length of the rectangle is x cm. The length of a diagonal of the rectangle is 8 crn. The perimeter of the rectangle is 20 cm

. Show that ia + 91 +b=0 where a and b are integers to be found.​

Mathematics
1 answer:
klemol [59]3 years ago
6 0

Answer:

x^2-10x+18=0

<em>a</em> = -10 and <em>b</em> = 18.

Step-by-step explanation:

Let <em>w</em> represent the width of the rectangle.

We are given that the perimeter of the rectangle is 20 cm, this means that:

20=2(x + w)

Let's put <em>w</em> in terms of <em>x</em>. Divide both sides by two:

10=x+w

And solve for <em>w:</em>

<em />w=10-x<em />

So, the rectangle measures <em>x</em> by (10 -<em> x</em>) cm.

<em />

According to the Pythagorean Theorem:

a^2+b^2=c^2

<em>a</em> and <em>b</em> are the legs and <em>c</em> is the hypotenuse.

Substitute <em>x</em> for <em>a, w</em> for <em>b</em>, and 8 for <em>c:</em>

<em />x^2+w^2=8^2<em />

Simplify and substitute:

x^2+(10-x)^2=64

Square:

x^2+(100-20x+x^2)=64

Isolate the equation. So:

2x^2-20x+36=0

Since the leading coefficient is one, divide both sides by two:

x^2-10x+18=0

Therefore, <em>a</em> = -10 and <em>b</em> = 18.

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