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Question 11:
a) If these two rectangles have the same area, determine the value of x.

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Question 11a If These Two Rectangles Have The Same Area Determine The Value Of X class=

Sagot :

Zarahaider4211idn

Answer:

x = 7

Step-by-step explanation:

Solving the Problem

We're told that the areas of both rectangles (the product of their respective side lengths) are equal.

This means that,

                                  (2x + 4)(x + 3) = (x + 5)(3x - 6).

To find x, we expand and rearrange.

                                   2x² + 10x + 12 = 3x² + 9x - 30

                                        10x + 12 = x² + 9x - 30

                                             12 = x² - x - 30

                                              0 = x² - x - 42

                                               0 = (x-7)(x+6)

                                                    x = 7, -6

To determine which is our answer can plug it into all of the side lengths, if any one of them is negative, then we eliminate that x value (side lengths of a shape are never negative).

x = 7:

2(7) + 4 = 18 (+)

7 + 3 = 10 (+)

7 + 5 = 12 (+)

3(7) - 6 = 15 (+)

x = -6:

2(-6) + 4 = -8 (-)
-6 + 3 = -3 (-)

-6 + 5 = -1 (-)

3(-6) - 6 = -24 (-)

So, our final answer is x = 7.

                         

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