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

★Solution:-

◕ Sum of perpendicular Sides is 196.

Then,

→ (x + y)² = 196

→ x + y = 14

→ y = 14 - x ......i)

◕ Area of triangle -

→ $\sf\dfrac{1}{2}$× base × height

→ $\sf\dfrac{1}{2}$ xy = 24

→ xy = 48

◕ Substituting eq...i) in this equation,

➳ x (14 - x) = 48

➳ 14x - x² = 48

➳ x² - 14x + 48 = 0

➳ x² - 8x - 6x + 48 = 0

➳ x (x - 8) - 6 (x - 8)

➳ x = 8 or 6

➳ y = 14 - x

➳ y = 14 - 8

➳ y = 6

➳ x - y = 8 - 6 = 2

➳ x + y = 8 + 6 = 14

∴ Hence,

$\boxed{\rm{\red{x+y=14}}}$

$\boxed{\rm{\green{x-y=2}}}$

______________________________

Answer 2

Answer:

Given

• Sum of perpendicular Sides is 196.

Then,

→ (x + y)² = 196

→ x + y = 14

→ y = 14 - x ......i)

Area of triangle -

$→ \sf\dfrac{1}{2}21 × base × height$

$→ \sf\dfrac{1}{2}21 xy = 24$

$\fbox{→ xy = 48}$

Substituting eq...i) in this equation,

➳ x (14 - x) = 48

➳ 14x - x² = 48

➳ x² - 14x + 48 = 0

➳ x² - 8x - 6x + 48 = 0

➳ x (x - 8) - 6 (x - 8)

➳ x = 8 or 6

➳ y = 14 - x

➳ y = 14 - 8

➳ y = 6

➳ x - y = 8 - 6 = 2

➳ x + y = 8 + 6 = 14

Therefore:-

• x + y = 14

• x - y = 2