A rectangle courtyard, the sides of which are in the ratio if $4 : 3$ , costs Rs. $600$ for paving at $50$ P per square metre. What is the diagonal of the courtyard?

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Solution

Area of the courtyard
$= \frac{T o t a l c o s t}{C o s t o f 1 s q . u n i t}$
$= \frac{600}{\frac{50}{100}} = 1200$ sq.m
Now $l : b = 3 : 4$ , let $l = 4 x$ and $b = 3 x$
$∴ 4 x \times 3 x = 1200$
or $x^{2} = 100$
$∴ l = 4 x = 4 = 4 \times 10 m = 40 m$
$b = 3 x = 3 \times 10 m = 30 m$
Diagonal $= \sqrt{l^{2} + b^{2}} = \sqrt{{(40)}^{2} + {(30)}^{2}} = \sqrt{2500}$
$= 50$ m

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A rectangle courtyard, the sides of which are in the ratio if 4:3, costs Rs.600 for paving at 50 P per square metre. What is the diagonal of the courtyard?

Area of the courtyard=TotalcostCostof1sq.unit=60050100=1200 sq.mNow l:b=3:4, let l=4x and b=3x∴4x×3x=1200or x2=100∴l=4x=4=4×10m=40mb=3x=3×10m=30mDiagonal =√l2+b2=√(40)2+(30)2=√2500=50 m

A rectangle courtyard, the sides of which are in the ratio if $4 : 3$ , costs Rs. $600$ for paving at $50$ P per square metre. What is the diagonal of the courtyard?