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Question

Find the length of the diagonal, whose length and width of a rectangle are in the ratio $$5:12$$. If the rectangle has an area of $$504 m^2$$.


A
19m
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B
29m
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C
39m
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D
49m
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Solution

The correct option is B $$39 m$$
The length and width of the rectangle are in a ratio $$5:12$$, so the sides can be written as $$5x$$ and $$12x$$.
So, Area $$= (5x).(12x)= 504$$
$$60x^2=504$$
$$x^2 = \dfrac{504}{60}$$
$$x^2 = 9$$
$$x = 3$$
Then length $$= 5x = 5 \times 3 = 15 m$$
width $$= 12x = 12 \times 3 = 36 m$$
Diagonal length of a rectangle $$= \sqrt{l^2+w^2}$$
$$= \sqrt{15^2+36^2}$$
$$= \sqrt{225+1296}$$
$$= \sqrt{1521}$$
$$= 39 m$$

Maths

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