Question

The altitude PM is drawn to the hypotenuse RQ of a right angled triangle PQR.

If PM = y cm, PR = x cm, RM = 4 cm and MQ = 5 cm, find the values of x and y​

Answer 1

$\huge❥{\underline{\mathtt{\red{A}\pink{N}\green{S}\blue{W}\purple{E}\orange{R}}}}$

In triangles PQS and PQR

∠P is common to both.

and ∠PSQ=∠PQR

Triangles PQS and PQR are equiangular

∴

PQ

PS

=

QR

QS

or, PS=

QR

PQ⋅QS

...(i)

Again, triangles QRS and PQR are equiangular

∴

QR

SR

=

PQ

QS

or, SR=

PQ

QS⋅QR

...(ii)

From eqns. (i) and (ii)

SR

PS

=

QR

PQ⋅QS

⋅

QR⋅QS/PQ

=

QR^2/PQ^2