Question

One side of a right triangle measures 20cm and the difference in lengths of its hypotenuse and other side is 8 cm. Find the measures of its unknown sides and calculate its area.

Answer 1

lenght of one side=20cm

let the unknow side be denoted as b and hypotenuse as h

h-b=8cm

h=b+8

Pythagoras theorem

height²+base²=hypotenuse ²

20²+b²=(b+8)²

400+b²=b²+(2*8*b)+8²

400+b²=b²+16b+64

400=16b+64

16b=400-64

16b=336

b=336/16

b=21cm

so h=21+8=29cm