Question

in a square pqrs PQ = 5 a - 17 cm and QR =2a + 4 find the length of the PS and PR

Answer 1

as pqrs is a square all sides will be equal,

So, PQ = QR = RS = PS

as PQ = QR

implies that 5a - 17 = 2a + 4

3a = 21

a = 21/7cm

a = 3cm

as a = 3cm

PQ = 5a - 17 = 5(3) -17 = -2cm

QR = 2a +4 = 2(3) + 4 = 10cm

Answer 2

Given,

In a square PQRS;

PQ = 5a - 17 cm

QR =2a + 4 cm

To find,

The length of the PS and PR.

Solution,

We can simply solve this mathematical problem using the following process:

As per mensuration;

The length of all the sides of a square is equal. Also, the angle at each vertex of a square is a right-angle.

Now,

in given square PQRS,

PQ = QR = RS = PS {Equation-1}

=> PQ = QR

=> (5a - 17) cm = (2a + 4) cm

=> 3a = 21

=> a = 7

Substituting the value of a in equation-1, we get:

PQ = QR = RS = PS = (2a + 4) cm

=> PQ = QR = RS = PS = 18 cm

Now,

In the square PQRS, on applying Pythagoras theorem in the right-angled triangle PQR right-angled at Q, we get;

(PQ)^2 + (QR)^2 = (PR)^2

=> (18)^2 + (18)^2 = (PR)^2

(from equation-1)

=> (PR)^2 = 2 x (18)^2

=> PR = 18√2 cm

Hence, the length PS and PR of the square PQRS are equal to 18 centimeters and 18√2 centimeters, respectively.