PQR is a triangle and PX is perpendicular to QR at X.
Given that PR= 6cm, RX=4cm and RQ=9cm, calculate PQ.
Leave your answer in surd form?
Did you make your sketch??
I get PX^2 + 4^2 = 6^2
PX =
now in the other triangle:
PQ^2 = 5^2 + PX^2 , but you know PX^2, so its easy from here
To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, we can use it to find the length of PQ.
Let's label the length of PQ as x. Based on the information given, we can set up the following equation:
PR^2 = PX^2 + RX^2
Substituting the given values, we have:
(6cm)^2 = PX^2 + (4cm)^2
36cm^2 = PX^2 + 16cm^2
Now, let's solve for PX:
20cm^2 = PX^2
Taking the square root of both sides, we get:
√(20cm^2) = √(PX^2)
√20cm = PX
Simplifying the square root of 20, which is the same as 4√5, we have:
PX = 4√5 cm
Now, we can find the length of PQ using the Pythagorean theorem again:
PQ^2 = PX^2 + QX^2
PQ^2 = (4√5 cm)^2 + (9 cm)^2
PQ^2 = 80 cm^2 + 81 cm^2
PQ^2 = 161 cm^2
Finally, taking the square root of both sides, we get:
√(PQ^2) = √(161 cm^2)
PQ = √161 cm
Therefore, the length of PQ in surd form is √161 cm.