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I don’t get how to do this please help!

I don’t get how to do this please help!-example-1
User Laronda
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1 Answer

3 votes

Answer:

Length = 5 cm

Width = 3 cm

Explanation:

Part (a)

Length L = c

(i) Width W = c- 2 (width is 2 cm less than width)

(ii) Area of the rectangle = L x W
= c(c - 2) = c² - 2c

Part (b)
Area is given as 15 cm²

Therefore, c²- 2c = 15

Part (c)

The equation for area from part (b) is

c² - 2c = 15

Carry 15 to the left side by subtracting 15 from both sides:
c²- 2c - 15 = 15 - 15

c²- 2c - 15 = 0

This is a quadratic equation which can be solved easily by factoring

The factors of the constant 15 are 5 and 3
The constant is product of the factors is -15; so one of the numbers is negative

The sum of the numbers is the coefficient of c

Since this -2, the numbers are -5 and 3

Therefore the factorization of the equation

c² - 2c - 15 = (c + 3)(c - 5)

And since c² - 2c - 15 = 0 this means (c + 3)(c - 5) = 0

So either c + 3 = 0 ==> c = -3 which can be rejected because length cannot be negative

This gives us
c - 5 = 0

Or c = 5

So length = 5 cm

Since width = c - 2

width = 5 - 2 = 3

Length = 5

Width = 3

User Jakeem
by
8.6k points

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