Question

On the two catheti of a right-angled triangle (with lengths a and b respectively) points P and Q respectively are chosen. Let K and H be the endpoints of the perpendicular lines from P and Q respectively, to the hypotenuse of the triangle. How big is the smallest possible value of KP + PQ + QH?

Answer 1

Answer:

$\huge{\fbox{\fbox{\bigstar{\mathfrak{\red{Answer}}}}}}$

In a right triangle the area of the square on the hypotenuse is equal to the sum of the areas of the squares of its remaining two sides.

(Length of the hypotenuse)2 = (one side)2 + (2nd side)2

In the given figure, ∆PQR is right angled at Q; PR is the hypotenuse and PQ, QR are

the remaining two sides, then

(PR)2 = PQ2 + QR2

(h)2 = p2 + b2

[Here h → hypotenuse, p → perpendicular, b → base]

Answer 2

$\huge\bold\red{Answer}$

♣️Refer To Attachment ♣️

I Hope It Helps You✌️