A rectangle carpet has an area of 120 square metres and a perimeter of 46 m. The length of its diagonal is:
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Step 1
given:
Area = 120 m^2
ie, l x b = 120 ---------------------( 1 )
Perimeter = 46 m
2 (l + b) = 46
l + b = 23
l = 23 - b ------------------- (2)
substitute (2) in (1)
(23 - b) b = 120
23 b - b^2 = 120
b^2 -23 b +120 = 0
(b-8) (b-15) = 0
b = 8, 15
so, l = 15, 8 (on sub. in (1))
so, the length of the rectangle = 15
breadth of the rectangle = 7
the diagonal of the rectangle = sq. root of (15^2 + 8^2)
= sq. root of 289
= 17 m
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