surface area of a rectangular pool

[apshara5]

Is the surface area of a rectangular pool lager than 1000 square feet.
1 the pool measure fifty feet diagonally
2 one side of the pool side measure 25 feet
ans :c

[Anurag@Gurome]

Is the surface area of a rectangular pool lager than 1000 square feet.
1 the pool measure fifty feet diagonally
2 one side of the pool side measure 25 feet

To determine the surface area of the rectangular pool we need the measures of two consecutive sides of the pool. None of the statements individually provide the required information.

But both statements together, we know length of the diagonal, d = 50 feet and measure of one side, a = 25 feet.

Hence, we can find the measure of the other side, b as follows,

• b = √(d² - a²)

Hence, required surface area = a*b = a*(√(d² - a²))
As we know a and d, we can calculate the area

The correct answer is C.

[shankar.ashwin]

A rectangular pool can be considered as a box(cuboid)

The SA of a cuboid is 2(LB+BH+HL)

(1) Diagonal measures 50.
Now the diagonal can be that of LB,BH or HL.

We can have 2 sides as say 35,35 where SA is > 1000
or we have a side measuring more than 49 and the other 1, where the SA<1000.

We can't say.

(B) only one side is given and obviously we can have both the cases possible.

Combined: We know one diagonal measures 50 and a side is 25. So the SA will be greater than 1000.

Hence C

[neelgandham]

Is surface are > 1000 ?

1) Diagonal = 50ft.

Say, a,b are the sides of the rectangle => a^2 + b^2 = 50^2 [spoiler]so 2(a+b) = ? Insufficient [/spoiler]

2)One side of the pool side measure 25 feet

Say a,b are the sides of the rectangle => 25^2 + b^2 = c^2 [spoiler]so 2(a+b) = ? Insufficient [/spoiler]

Using 1 and 2 [spoiler]a =25, c=50, b =25 square(3) Hence option C[/spoiler]