If the width of rectangle is 5 cm more than one-half of its length the perimeter is 70 cm, what are the dimensions of the rectangle?

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If the width of rectangle is 5 cm more than one-half of its length the perimeter is 70 cm, what are the dimensions of the rectangle?

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Answer 1 · 2016-12-04T16:18:54

The length is 20 cm and the width is 15 cm

Explanation:

First, let's call the width of our rectangle $w$ $w$ and the length $l$ $l$ .

From the problem we know:

$w = \frac{1}{2} l + 5$ $w = 1/2l + 5$

We also know the formula for the perimeter of a rectangle is:

$p = 2 \cdot l + 2 \cdot w$ $p = 2*l + 2*w$

So we can substitute $70$ $70$ for $p$ $p$ which is given in the problem and we can also substitute $\frac{1}{2} l + 5$ $1/2l + 5$ for $w$ $w$ and then solve for $l$ $l$ :

$70 = 2 \cdot l + 2 \cdot (\frac{1}{2} l + 5)$ $70 = 2*l + 2*(1/2l + 5)$

$70 = 2 l + 1 l + 10$ $70 = 2l + 1l + 10$

$70 = 3 l + 10$ $70 = 3l + 10$

$70 - 10 = 3 l + 10 - 10$ $70 - 10 = 3l + 10 - 10$

$60 = 3 l$ $60 = 3l$

$\frac{60}{3} = \frac{3 l}{3}$ $60/3 = (3l)/3$

$20 = l$ $20 = l$

Now we can substitute $20$ $20$ for $l$ $l$ in the formula for $w$ $w$ to find the width:

$w = \frac{1}{2} 20 + 5$ $w = 1/2 20 + 5$

$w = 10 + 5$ $w = 10 + 5$

$w = 15$ $w = 15$

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If the width of rectangle is 5 cm more than one-half of its length the perimeter is 70 cm, what are the dimensions of the rectangle?

1 Answer

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