Question

pqrs is a rectangle such that PQ equal to 2 PS and the diagonal PR is equal to 15 M find the perimeter of the rectangle

Answer 1

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Answer 2

Answer:

18√5 meters.

Step-by-step explanation:

PQRS is a rectangle,

⇒ PQ = SR, PS = QR,

Also, the perimeter of the rectangle = 2 (Sum of any adjacent sides)

⇒ P = 2(PQ + QR)

⇒ P = 2(PQ + PS) ---------(1),

Given,

PQ = 2PS,

And, diagonal PR = 15 m,

$\implies \sqrt{(PQ)^2+(PS)^2} = 15$

$(PQ)^2+(PS)^2=225$

$(2PS)^2+(PS)^2=225$

$4 PS^2+PS^2=225$

$5PS^2=225$

$PS^2=45\implies PS=\sqrt{45}=3\sqrt{5}\text{ meters}$

Thus, PQ = 6√5 meters.

Hence, the perimeter of the rectangle,

P = 2(6√5+3√5) = 2(9√5) = 18√5 meters.