Given the rectangular area 78 cm².
Find X
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Given the rectangular area 78 cm².
Find X
We know that the area of a rectangle is equal to its length multiplied by its width.
We begin by writing an equation with the available data.
We then use the distributive property to solve the equation.
That is, we multiply each of the terms inside of the parentheses by 3:
We move 21 to the other side and use the appropriate sign:
Lastly we divide both sides by 3:
\( 140-70= \)
Because the width is 3 and the length is (x + 7), not just x! You need to set up the equation first, then solve step by step.
The distributive property helps us expand into . This removes the parentheses so we can solve the linear equation normally.
It doesn't matter! In rectangles, area = length × width works the same as area = width × length. The important thing is identifying which measurement goes with which label.
Check your arithmetic! In this problem, x should be positive since it represents part of a length measurement. Negative lengths don't make sense in real-world rectangle problems.
We want to isolate the term with x. Since we have , subtracting 21 from both sides gives us , which is easier to solve.
Substitute x = 19 back into the original setup: length = 19 + 7 = 26 cm, width = 3 cm. Check: cm² ✓
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