Question

A right-angled triangle, whose legs are in the ratio 5:12, has the hypotenuse 26cm. What is the length of the legs? ( with working and all steps)

Answer 1

Answer:

10cm and 24cm respectively.

Step-by-step explanation:

Let the ratios be 5x and 12x.

Hypotenuse = 26cm

Now,

(5x)² + (12x)² = (26)² [Pythagoras Theorem]

=) 25x² + 144x² = 676cm²

=) 169x² = 676cm²

=) x² = 676/169

=) x² = 4

=) x = 2 (square root of 4)

Perpendicular leg (height) = 5 × 2 = 10cm

Linear leg (base) = 12 × 2 = 24 cm

Hence, the legs are 10cm and 24cm respectively.