Question

PQRS is a rectangle and QTR is a triangle whose 2 angles are 60 degree.If QT=RT=7,find the perimeter and diagonal of the rectangle if the length is 3 more than 3 times the breadth.
Plz help me

Answer 1

Answer:

Perimeter=62 cm and Diagonal=25 cm.

Step-by-step explanation:

Given that PQRS is a rectangle whose ∠P =∠Q =∠R =∠S =90°

Again given that QTR is a triangle where ∠RQT=∠QRT is 60° each.

So, ∠RTQ = (180°-60°-60°) =60°.

Hence, ΔQTR is an equilateral triangle where QT= TR= RQ = 7 cm (Given)

So, the breadth of the rectangle PQRS = RQ= 7 cm =PS ..... (1)

Now, as per condition is given, the length of rectangle PQRS is 3 more than 3 times the breadth.

So, length= PQ or RS =3*7+3= 24 cm. ...... (2)

Therefore, the perimeter of the rectangle PQRS =2*(length+breadth)=2*(24+7) =62 cm. {From equation (1) and (2)}  

(Answer)

Again, to get the length of diagonal of rectangle PQRS, join points P and R.

Now, ΔPSR is a right-angled triangle with hypotenuse PR and ∠PSR =90°

So, applying Pythagoras Theorem, diagonal PR=√(PS²+SR²)= √(7²+24²) =25 cm {From equation (1) and (2)}

(Answer)