Question

29. One side of right triangle measures 126 m and the difference in length of its hypotenuse and other side is 42 m.
find the measure of its two unknown sides and calculate its area.​

Answer 1

Answer:

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}hypotenuse

2

=s1

2

+s2

2

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

2

=126+x

2

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

17.64+0.84x+x

2

=

126+x

2

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=

0.84

108.36

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.

Answer 2

Answer:

Sides: 126 cm, 168 cm, 210 cm

Area = 10584 cm²

Step-by-step explanation:

Let the other side be x cm.

Then the hypotenuse will be x + 42 cm.

According to Pythagoras Theorem,

$h^{2}=p^{2}+b^{2} \\or,(x+42)^{2} = x^{2} + 126^{2}\\or,x^{2} + 84x + 1764 = x^{2} + 15876\\or, 84x +1764=15876\\or, 84x=15876-1764\\or, 84x=14112\\or,x=\frac{14112}{84} \\or,x=168$

So the other side is equal to 168 cm.

Then, we know,

$h=x+42\\or, h = 168+42 \\or, h=210$

Therefore, the hypotenuse is equal to 210 cm.

By the formula of area of a triangle, we know,

a = $\frac{1}{2}$ × $p$ × $b$

or, a =  $\frac{1}{2}$ × 168 cm × 126 cm

or, a = 63 × 126 cm²

or, a = 10584 cm²