Question

area of triangle is 24 cm square and the square of sum of the perpendicular side is 196. taking sides as x and y find x+y, find x-y, length of sides

Answer 1

Answer:

According to the condition:

Sum of perpendicular sides is 196:

(x+y)^2=196

x+y=14

y=14-x --(i)

Area of the triangle:

0.5*xy=24

xy=48

Substituting (i) in this equation:

x(14-x) =48

x^2-14x+48=0

x^2-8x-6x+48=0

x(x-8)-6(x-8) =0

(x-6) (x-8) =0

x=8 or 6

When x=8, then y will be 6 and vice-versa.

When assuming x is the longer side:

x-y=8-6

x-y=2

Thus their sum is 14 and their difference is 2.

Answer 2

Answer:

sqrt(292), 10, sqrt(73) + 5, sqrt(73) -5

Step-by-step explanation:

Area of trianhle = (1/2)xy = 24

=> 2xy = 96..(i)

x^2 + y^2 = 196 ..(ii)

Adding (i) and (ii)

x^2 + y^2 + 2xy = 292

=> (x + y)^2 = 292

=> x + y = sqrt(292) ...(iii)

Subtracting (i) from (ii)

x^2 + y^2 - 2xy = 100

=> ( x - y)^2 = 100

=> x - y = 10 ...(iv)

Adding (iii) and (iv)

2x = 10 + sqrt(292)

=> x = 5 + sqrt(73)

putting value of x in (iv)

y = sqrt(73) - 5