Advertisements
Advertisements
प्रश्न
The length of the sides forming a right angle in a triangle are 5x cm and (3x-1) cm. If the area of the triangle is 60cm2, find the hypotenuse.
उत्तर
Area of a triangle = `("Height" xx "Base")/2`
Here, Height and base are 5x and (3x-1) and the area is 60
Hence , `5x xx (3x - 1) xx 1/2 = 60`
⇒ 15x2 - 5x = 120
⇒ 3x2 - x -24 = 0
⇒ 3x2 - 9x + 8x - 24 = 0
⇒3x (x - 3) +8(x - 3) = 0
⇒ (3x + 8)(x - 3) = 0, hence x = 3.
Sides are 5 x 3 and 3 x 3-1= 15 and 8 ems.
⇒ Hence, h2= 152 + 82 = 289
Hypotenuse = 17 cms.
APPEARS IN
संबंधित प्रश्न
Solve for x
:`1/((x-1)(x-2))+1/((x-2)(x-3))=2/3` , x ≠ 1,2,3
Solve the following quadratic equations by factorization:
`sqrt2x^2-3x-2sqrt2=0`
The difference of two numbers is 4. If the difference of their reciprocals is 4/21. Find the numbers.
For the equation given below, find the value of ‘m’ so that the equation has equal roots. Also, find the solution of the equation:
(m – 3)x2 – 4x + 1 = 0
Solve the following quadratic equations by factorization:
`(2x – 3)^2 = 49`
Solve for x:
4x2 + 4bx − (a2 − b2) = 0
If −5 is a root of the quadratic equation\[2 x^2 + px - 15 = 0\] and the quadratic equation \[p( x^2 + x) + k = 0\] has equal roots, find the value of k.
If one root of the equation 4x2 − 2x + (λ − 4) = 0 be the reciprocal of the other, then λ =
Solve the following equation: (x-8)(x+6) = 0
Car A travels x km for every litre of petrol, while car B travels (x + 5) km for every litre of petrol.
(i) Write down the number of litres of petrol used by car A and car B in covering a distance of 400 km.
(ii) If car A uses 4 litres of petrol more than car B in covering 400 km. write down an equation, in A and solve it to determine the number of litres of petrol used by car B for the journey.
