If the diagonal of rectangle \(Z\) is \(d,\) and the perimeter of rectangle \(Z\) is \(p,\) what is the area of rectangl

M7MBA wrote: ↑

Sun Jun 21, 2020 2:21 pm

If the diagonal of rectangle \(Z\) is \(d,\) and the perimeter of rectangle \(Z\) is \(p,\) what is the area of rectangle \(Z,\) in terms of \(d\) and \(p?\)

(A) \(\dfrac{d^2 – p}3\)
(B) \(\dfrac{2d^2 – p}2\)
(C) \(\dfrac{p – d^2}2\)
(D) \(\dfrac{12d^2 – p^2}8\)
(E) \(\dfrac{p^2 – 4d^2}8\)

[spoiler]OA=E[/spoiler]

Source: Manhattan GMAT

Say the length and the breadth of the rectangle are l and b, respectively.

=> Area = lb;
Perimeter = 2(l + b) = p => l +b = p/2

and, \(d^2 = l^2 + b^2\)

Above can be rewritten as \(d^2 = l^2 + b^2 + 2lb – 2lb = (l + b)^2 – 2lb = (p/2)^2 – 2*Area\)

Area = \(p^2/8 - d^2/2 = (p^2-4d^2)/8\)

Correct answer: E

Hope this helps!

-Jay
_________________
Manhattan Review GMAT Prep

Locations: Manhattan SAT | GMAT Practice Questions | GRE Practice Test | LSAT Info | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.