Question

area of a right angled triangle is 240m² and side other than hypotenuse is 30m .find the perimeter of the triangle.

Answer 1

in a right triangle the area is 1/2base x height.

 240= 1/2 x base x 30  .    thus base =16m

By Pythagoras theorem (Hypotenuse)2 = (30)2  + (16)2 Thus,

hypotenuse = whole root of 1156 =  34m

Perimeter of the triangle = 34 +30 + 16        thus,   Perimeter = 80m             

Answer 2

The perimeter of the triangle is 80 meters.

GIVEN

Area of a right angled triangle is 240m² and side other than hypotenuse is 30m.

TO FIND

Perimeter of the triangle.

SOLUTION

We can simply solve the above problem as follows;

Let ABC is a triangle.

where,

∠B = 90°

AC = Hypotenus

AB = Base

BC = perpendicular.

Now, It is given that the side other than the hypotenus = 30 m

So, Either AB or BC = 30m

Let, AB = 30 m

Now,

Area of triangle = (1/2)× Base × Height

240 = (30 × BC)/2

480 = 30BC

BC = 480/30 = 16 m

Applying the pythagorus theorem in ΔABC

AC² = AB² + AB²

AC² = 1156

AC = √1156 = 34m

Now,

Perimeter of a traingle = AB + BC + AC =30 + 16 + 34 = 80 meter.

Hence, The perimeter of the triangle is 80 meters.

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