The base of an isosceles triangle measures 24cm and its area is 192cmsq. Find its perimeter?

 

The base of a triangular field is three times its altitude. If the cost of sowing the field at Rs 58 per hectare is Rs 783, find its base and height?

 

The difference between the sides at right angles in a right- angled triangle is 7 cm. The area of the triangle is 60 cmsq. Find its perimeter?

 

1. Let ABC be the isosceles triangle in which AB = AC and AD be the altitude so that BD = DC.

We have,  Area = 1/2 X Base X Altitude = 192 cm²

So, Altitude = 16 cm.

So, AB² = AD² + BD²

=> AB² = 16² +  (BC/2)² = 16² +  (24/2)²  =  16² +  12²    

=> AB = 20 cm

So, AC = 20 cm

So, Perimeter of the triangle = 20 + 20 + 24 = 64 cm.

3. Given the diffrence between the sides  is 7

Let one side be x

therefore the other side is 7+x .

ACCORDING TO QUESTION

area triangle is 60cmsq

so, ar of triangle is = 1/2 * base * height

=> 1/2 * x * x+7 =  x²+ 7x / 2 = 60

=>  x²+ 7x  = 120

=>  x²+ 7x  - 120 = 0  =>  x² + 15x - 8x - 120 = 0

=>  x ( x + 15 ) - 8 ( x + 15 ) = 0

=>  ( x + 15 )  ( x - 8 ) =  0  =>  x=  -15  ( or )  x=  8

so, one side of a triangle is 8cm  &  other side is 15 cm  , HYPOTENUSE is  8² + 15²  = 17cm

hence perimeter is  8+ 15 + 17 =  40cm

HOPE U GOT IT

thanks to both of you!!!!!!