Question

in a right angled triangle one of the perpendicular sides is 6cm more than the other side. if the area is 36cm^2 find the length of perpendicular sides​

Answer 1

${ \bf{ \red{ \underline{ \purple{ \underline{Given \: data}}}}}:-}$

๏ In a right angled triangle one of the perpendicular sides is 6cm more than the other side.

๏ The area is 36cm² .

${ \bf{ \red{ \underline{ \purple{ \underline{Solution}}}}}:-}$

Let, height of right angle triangle be x and base of right angle triangle be y.

Let, first perpendicular side be x and second perpendicular side be y.

{According to given}

→ x = y + 6 .... ( 1 )

Now, we use formula of area of right angle triangle.

→ Area of right angle triangle

= ½ × base × height

{According to given}

→ 36 = ½ × x × y

{from ( 1 )}

→ 36 = ½ × (y + 6) × y

→ 36 = ½ × (y² + 6y)

→ 36 × 2 = y² + 6y

→ 72 = y² + 6y

→ y² + 6y - 72 = 0

Now, { we use factorization method}

→ y² + 6y - 72 = 0

→ y² + 12y - 6y - 72 = 0

→ y ( y + 12 ) - 6 ( y + 12 ) = 0

→ ( y - 6 ) ( y + 12 ) = 0

→ y - 6 = 0 or y + 12 = 0

→ y = 6 or y = - 12

We know the length of the side of right angle triangle is never negative { is not negative } Hence, y ≠ - 12 & y = 6

Now, put value of y in equation ( 1 )

→ x = y + 6

→ x = 6 + 6

→ x = 12

Hence, length of perpendicular sides are 12 cm and 6 cm. or height of right angle triagle is 12 cm and base of right angle triagle is 6 cm.