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
B
29m
C
39m
D
49m

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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