Question

In rectangle PQRS, PR = 25 and the area is 168. What is the measure of PQ? (IT'S NOT 6.72)

Answer 1

length of PQ is 7cm Or 24 cm

Answer 2

Given:

In rectangle PQRS, PR = 25 and the area is 168.

To find:

The measure of PQ

Solution:

In rectangle PQRS, let,

"PQ = l" → length of the rectangle

"QR = b" → breadth of the rectangle

The area of the rectangle PQRS = 168

∴ $l \times b = 168$   [since the area of rectangle = length × breadth]

The diagonal of the rectangle, PR = 25

∴ $PR = \sqrt {l^2 + b^2}$

$\implies 25^2 = l^2 + b^2$

$\implies 625 = l^2 + b^2 - 2lb + 2lb$

$\implies 625 = (l^2 + b^2 + 2lb) - 2lb$

$\implies 625 = (l + b)^2 - 2lb$

putting the value of l × b, we get

$\implies 625 = (l + b)^2 - (2\times 168)$

$\implies 625 = (l + b)^2 - 336$

$\implies 961 = (l + b)^2$

$\implies l + b = 31$

$\implies l + \frac{168}{l} = 31$

$\implies l^2 + 168 = 31l$

$\implies l^2 -31l + 128 = 0$

$\implies l^2 -24l - 7l + 128 = 0$

$\implies l (l - 24) - 7 (l-24) = 0$

$\implies (l - 24)(l - 7)=0$

$\implies \bold{l = 24 \:or\:7}$

Thus, PQ is → 24 cm or 7 cm.

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