Question

P Q x metres R A wire of length 5 metres is to be bent to form the hypotenuse and base of a right-angled triangle PQR, as shown in the diagram. Let the length of the base QR be x metres. i. What is the length of the hypotenuse PQ in terms of x? ii. Show that the area of the triangle PQR is 1/2 x sqrt(25 - 10x) square metres. iii. What is the maximum possible area of the triangle?

          P
Q
x metres
R
A wire of length 5 metres is to be bent to form the hypotenuse and base of a right-angled triangle PQR, as shown in the diagram. Let the length of the base QR be x metres.
i. What is the length of the hypotenuse PQ in terms of x?
ii. Show that the area of the triangle PQR is 1/2 x sqrt(25 - 10x) square metres.
iii. What is the maximum possible area of the triangle?

P
Q
x metres
R
A wire of length 5 metres is to be bent to form the hypotenuse and base of a right-angled triangle PQR, as shown in the diagram. Let the length of the base QR be x metres.
i. What is the length of the hypotenuse PQ in terms of x?
ii. Show that the area of the triangle PQR is 1/2 x sqrt(25 - 10x) square metres.
iii. What is the maximum possible area of the triangle?

Added by Nicholas R.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Jerelyn Nevil

05/11/2023

Step 1

Since QR is x meters, the remaining length of the wire will be used for the hypotenuse PQ. Show more…

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A wire of length 5 metres is to be bent to form the hypotenuse and base of a right-angled triangle PQR, as shown in the diagram. Let the length of the base QR be x metres. i. What is the length of the hypotenuse PQ in terms of x? ii. Show that the area of the triangle PQR is 1/2 x sqrt(25 - 10x) square metres. iii. What is the maximum possible area of the triangle?