Pythagoras Theorem

Question

In the figure, PQ=13cm, PR=12cm, PS=18cm and PR and QR are perpendicular to QS and PS respectively. Calculate the length of QS.

(P is at the top point of the triangle, Q is at the bottom left and S is at the bottom right. Point T is between point P and S. Point R is between point Q and S. QTS and PRS are right angled triangles. Angle PRS and QTS are right angles.)

 

please show the full working and answers.

Answer 1

Hi Amy,

 

I hope I drew your figure correctly. In my figure, I am seeing two right triangles PRQ and PRS that share a common side PR. If I drew this correctly, then QS = QR + RS.

 

We need to find QR and RS separately by applying the Pythagorean theorem. Let's apply the Pythagorean theorem to triangle PRQ:

 

(QR)² + (PR)² = (PQ)²

 

So,

 

QR = sqrt[(PR)² = (PQ)²] = sqrt[13² - 12²] = sqrt[25] = 5, where sqrt stands for square root

 

So, QR = 5

 

We now apply the Pythagorean theorem to triangle PRS:

 

(RS)² + (PR)² = (PS)²

 

So,

 

RS = sqrt[(PS)² - (PR)²] = sqrt[18² - 12²] = sqrt[180] = 6√5

 

So, QS = QR + RS

 

QS = 5 + 6√5 = 18.4