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The diagonal of a rectangle field is 17 ...

The diagonal of a rectangle field is 17 m and its perimeter is 46 m. What is the area of the field ?

A

`132 m^(2)`

B

`120 m^(2)`

C

`112 m^(2)`

D

`289 m^(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
Let the length of rectangular field = l m and breadth = b m
Then, diagonal = `sqrt(l^(2) + b^(2))`
`rArr sqrt(l^(2) + b^(2)) = 17`
`rArr l^(2) + b^(2) = 289`………(i)
According to the question,
Perimeter, = 46 m
`rArr 2(l+b) = 46`
`rArr l + b = 23`........(ii)
On squaring both sides,
`(l+b)^(2) = (23)^(2)`
`rArr l^(2) + b^(2) + 2lb = 529`
`rArr 289 + 2lb = 529` [`therefore` From Eq. (i)]
`rArr 2lb = 529 - 289 = 240`
`therefore lb =240/2 = 120`
`therefore` Area of rectangle `=lb = 120 m^(2)`
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