Question

Consider a right angle triangle where the length of the shorter leg is one third of the length of its hypotenuse. If the length of the shorter leg is 7 cm, then calculate the area of thetriangle in square cm.

Answer 1

Length of shorter leg is 7cm Length of hypotenuse is 3×7=21cm Length of longer leg is square root of (21×21 - 7×7)= 19.8cm ( By pythagauras theorem) area of triangle=base × height /2 = 7× 19.8/2 = 16.29 Square cm

Answer 2

Answer:

The area of the triangle is 69.296 $cm^{2}$.

Step-by-step explanation:

• Area of right angle triangle be x $cm^{2}$

• Let the base(shorter leg) be b, height  h.

• So, the Area of the triangle = $\frac{1}{2}$ × b × h

• Let the right angle triangle be ABC where AB is the height, BC is the base and C is the hypotenuse.

• So, the Area of the triangle = $\frac{1}{2}$ × BC × AB

• Now, BC = $\frac{1}{3}$ of AC

       and   BC = 7 cm

• So, AC = 3 × BC = 3 × 7 cm. = 21 cm.

To calculate the height AB we can use Pythagoras theorem:

$AB^{2}$ + $BC^{2}$ = $AC^{2}$

$AB^{2}$ =  $AC^{2}$ -  $BC^{2}$ = $21^{2}$ - $7^{2}$ = 28 × 14 = 392

AB = $\sqrt{392}$ = 19.798 cm

So, the Area of the triangle = $\frac{1}{2}$ × BC × AB

                                             =  $\frac{1}{2}$ × 7 cm × 19.798 cm

                                             = 69.296 $cm^{2}$

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