Question

One side of a right angled triangle measures 126 m . And the difference in length of its hypotenuse and other side is 42 cm. find the measure of its two unknown sides and calculate its area. Verify the results using Heron's formula.

Answer 1

hi!
here's your answer!

s1 = 126m

hypotenuse - s2 = 42cm = 0.42m

Let the s2 be x.

hypotenuse - x = 0.42

hypotenuse = 0.42 + x

By Pythagoras theorem.

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

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

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

$17.64 + 0.84x = 126$
$0.84x = 126 - 17.64$

$0.84x = 108.36$

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

$x = 129$

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.

Answer 2

$\huge\mathbb{Heya}$

$\huge\boxed{Answer}$

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.