Question

in triangle OPQ right angle at P,OP=7cm OQ-PQ=1cm find thirdside

Answer 1

given:-
OPQ is rt angled at P .
OP=7cm
OQ-PQ=1cm
so, OQ = 1 + PQ
BY PYTHAGORUS THEOREM,
OQ^2=OP^2+PQ^2
(1+PQ)^2= 7^2 + PQ^2
1 + PQ^2+2PQ= 49 + PQ^2
2PQ= 48
PQ=24cm
OQ= 25cm

Answer 2

Answer:

The length of PQ is 24 cm and the length of OQ is 25 cm.

Step-by-step explanation:

It is given that in triangle OPQ right angle at P,OP=7cm, OQ-PQ=1cm.

Since the difference of OQ and PQ is 1, therefore OQ is 1 more than PQ.

Let the length of PQ be x cm. So, the length of OQ is x+1 cm.

Using Pythagoras theorem,

$OQ^2=PQ^2+OP^2$

$(x+1)^2=x^2+7^2$

$x^2+2x+1=x^2+49$

$2x+1=49$

$2x=49-1$

$2x=48$

$x=24$

The value of x is 24. So, the length of PQ is 24 cm.

The length of OQ is

$x+1=24+1=25$

The length of OQ is 25 cm.

Therefore the length of PQ is 24 cm and the length of OQ is 25 cm.