Question

one side of right triangle measure 126 cm and the difference in lengths of its hypotenuse and other side is 42 cm find the measure of its two unknown sides and calculate its area

Answer 1

s=168cm, area=10584cm

Answer 2

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step - by - step explanation

s1 = 126m

hypotenuse - s2 = 42cm = 0.42m

Let the s2 be x.

hypotenuse - x = 0.42

hypotenuse = 0.42 + x

By Pythagoras theorem.

${hypotenuse}^{2} = {s1}^{2} + {s2}^{2}$

${(0.42 + x)}^{2} = 126 + {x}^{2}$

$\begin{lgathered}17.64 + 0.84x + {x}^{2} = \\ 126 + {x}^{2}\end{lgathered}$

17.64 + 0.84x = 12617.64+0.84x=126

0.84x = 126 - 17.640.84x=126−17.64

0.84x = 108.360.84x=108.36

x = $\frac{108.36}{0.84}$x=

x = 129x=129

so

s2 = 129m

hypotenuse = x + 0.42

hypotenuse = 129 + 0.42

hypotenuse = 129.42m

Area of right angled triangle

=1/2 × product of perpendicular sides

=1/2 × 126 × 129

= 63 × 129

= 8127 metre sq.

Therefore,

The area of right angled triangle is 8127sq.m.