Mathematics

Problem

Two triangles

\triangle PQR

and

\triangle STU

are each right-angled at

Q

and

T

respectively. It is given that

PR = SU = 13\,\text{cm}

and

PQ = ST = 5\,\text{cm}

. a. (a) Prove that

\triangle PQR \cong \triangle STU

. b. (b) Find the lengths of

QR

and

TU

. c. (c) Determine the perimeter of

\triangle STU

. (Give your answer correct to one decimal place if necessary.)

Intuitive explanation

Both triangles are right-angled with the same hypotenuse length (13 cm) and one matching leg (5 cm). The key insight is to use the Pythagorean theorem to find the third side of each triangle—you'll discover that both missing legs have the same length, which means the triangles are congruent. This congruence tells you that all corresponding sides and angles must be equal.

Intuitive explanation

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