Question

hypotenuse or a right angled triangle is 29cm long its area is 210cm square calculate length of perpendicular sides​

Answer 1

Answer:

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Answer 2

Answer:

The length of the perpendicular sides of the right angled triangle is 20 and 21.

Step-by-step explanation:

$Hypotenuse^{2} = a^{2} +b^{2}$

Where, a and b are other two sides of the triangle.

Area of the triangle= $\frac{1}{2} \times ab$ = 210--------(1)

We are given that hypotenuse = 29

Also, $(a^{2} +b^{2}+2ab) = (a+b)^{2}$------(2)

From equation (1) we get,

ab = 420

2ab = 840 -------(3)

Also, $a^{2} +b^{2}=29^{2}$------(4)

Substituting (3) and (4) in (2),

$(a+b)^{2}$= $29^{2}+840$

= 841+840

=1681

=$41^{2}$

∴

(a+b)=41

Also,  $\frac{1}{2} \times ab$  = 210

Using trial and error method, we can assume the value of the sides to be 20 and 21

∴

The length of the perpendicular sides of the right angled triangle is 20 and 21.

The correct answer is 20 and 21.