A rectangle has a perimeter of 50 cm. If the ratio of its length to its width is 3:2, find the length of the rectangle?

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A rectangle has a perimeter of 50 cm. If the ratio of its length to its width is 3:2, find the length of the rectangle?

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Answer 1 · 2018-08-01T09:07:58

Length is $15 c m .$ $15cm.$ and width is $10 c m .$ $10cm.$

Explanation:

As length and width are in the ratio of $3 : 2$ $3:2$ , let these be $3 x$ $3x$ and $2 x$ $2x$

then perimeter is $2 \times (3 x + 2 x) = 2 \times 5 x = 10 x$ $2xx(3x+2x)=2xx5x=10x$

Hence $10 x = 50$ $10x=50$

or $x = \frac{50}{10} = 5 c m .$ $x=50/10=5cm.$

and length is $3 \times 5 = 15 c m .$ $3xx5=15cm.$ and width is $2 \times 5 = 10 c m .$ $2xx5=10cm.$

Answer 2 · 2018-08-01T09:22:09

Length $l = 15 c m$ $l =15cm$

Explanation:

Perimeter #(P) is the total distance around the sides.

Let length $= l$ $= l$ and width $= w$ $= w$

$P = 2 l + 2 w$ $P = 2l + 2w$ .....(1)

We are told that the ratio of $l$ $l$ to $w$ $w$ is $3 : 2$ $3:2$ so

$\frac{l}{w} = \frac{3}{2}$ $l/w = 3/2$

$l = \frac{3}{2} w$ $l = 3/2w$ .....(2)

Substitute for $l$ $l$ in (1)
$P = 2 \cdot (\frac{3}{2} w) + 2 w = 5 w$ $P = 2*(3/2w) + 2w = 5w$

But $P = 50 c m$ $P = 50cm$ so
$5 w = 50 c m$ $5w = 50cm$
$w = 10 c m$ $w = 10 cm$

Substitute $w = 10$ $w = 10$ into (2)
$l = \frac{3}{2} \cdot 10 = 15$ $l = 3/2*10 =15$

Answer 3 · 2018-08-01T09:24:24

$length = 15 cm$ $"length "=15" cm"$

Explanation:

$sum the parts of the ratio 3 + 2 = 5$ $"sum the parts of the ratio "3+2=5$

$P = 2 (l + b) = 50$ $P=2(l+b)=50$

$l + b = \frac{50}{2} = 25$ $l+b=50/2=25$

$\frac{25}{5} = 5 \leftarrow 1 part$ $25/5=5larrcolor(blue)"1 part"$

$length (l) = 5 \times 3 = 15 cm$ $"length (l)"=5xx3=15" cm"$

$breadth (b) = 5 \times 2 = 10 cm$ $"breadth (b)"=5xx2=10" cm"$

$P = 2 (15 + 10) = 2 \times 25 = 50 cm$ $P=2(15+10)=2xx25=50" cm"$

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A rectangle has a perimeter of 50 cm. If the ratio of its length to its width is 3:2, find the length of the rectangle?

3 Answers

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