The sides of a right-angled triangle containing the right angle are $4 x$ cm and $(2 x - 1)$ cm. If the area of the triangle is $30$ $c m^{2}$ ; calculate the lengths of its sides.

Open in App

Solution

area $\Rightarrow 30 c m^{2} = \frac{1}{2} (2 x - 1) (4 x)$
$60 = (4 x) (2 x - 1)$
$15 = x (2 x - 1)$
$2 x^{2} - x - 15 = 0$
$2 x^{2} - 6 x + 5 x - 15 = 0$
$2 x (x - 3) + 5 (x - 3) = 0$
$\Rightarrow x = 3, x = \frac{- 5}{2}$
since x cannot be negative
$x = 3$
$∴ A B = (2 x - 1) = 5 c m$
$A C = 4 x = 12 c m$
$B C = \sqrt{A B^{2} + A C^{2}} = \sqrt{25 + 144} + \sqrt{169} = 13 c m .$
$∴$ the sides are $5 c m, 12 c m$ and $13 c m$

Suggest Corrections

Similar questions

Q. The sides of a right triangle containing the right angle are

(5 x) c m

and

(3 x - 1) c m

. If area of triangle be

60 {c m}^{2}

, calculate the length of the sides of the triangle.

Q. The sides of a right-angled triangle containing the right angle are

5 x

cm and

3 x - 1

cm. If its area is

60 c m^{2}

, find its perimeter.

Q. The sides (in cm) of a right angle triangle containing right angle are

5 x

and

(3 x - 1)

. If the area of the triangle is

60 c m^{2}

. Find its perimeter.

Q. The side of a right triangle containing right angle are

5 c m

and

(3 x - 1) c m

.If area of tiangle is

60 c m^{2}

, find sides of triangle.

The side of right angle triangle containing right angle is 5x and (3x-1 ) cm. Calculate the length of the hypotenuse of the triangle if it's area is 60cm square.

Join BYJU'S Learning Program

The sides of a right-angled triangle containing the right angle are 4xcm and (2x−1)cm. If the area of the triangle is 30cm2; calculate the lengths of its sides.

area ⇒30 cm2=12(2x−1)(4x)60=(4x)(2x−1)15=x(2x−1)2x2−x−15=02x2−6x+5x−15=02x(x−3)+5(x−3)=0⇒x=3,x=−52since x cannot be negative x=3∴AB=(2x−1)=5 cmAC=4x=12 cmBC=√AB2+AC2=√25+144+√169=13cm.∴ the sides are 5 cm, 12 cm and 13 cm

The sides of a right-angled triangle containing the right angle are $4 x$ cm and $(2 x - 1)$ cm. If the area of the triangle is $30$ $c m^{2}$ ; calculate the lengths of its sides.