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.
Advertisements
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
A two-digit number is such that the products of its digits is 8. When 18 is subtracted from the number, the digits interchange their places. Find the number?
`x^2-4x+1=0`
Solve the following quadratic equations by factorization: \[\frac{5 + x}{5 - x} - \frac{5 - x}{5 + x} = 3\frac{3}{4}; x \neq 5, - 5\]
A two digit number is such that its product of its digit is 18. When 63 is subtracted from the number, the digits interchange their places. Find the number.
An aeroplane travelled a distance of 400 km at an average speed of x km/hr. On the return journey the speed was increased by 40 km/hr. Write down the expression for the time taken for
The outward journey
Solve the following equation by factorization:
`x^2 - (1 + sqrt(2))x + sqrt(2) = 0`
Solve the following equation by factorization
`x^2/(15) - x/(3) - 10` = 0
Find the values of x if p + 1 =0 and x2 + px – 6 = 0
Mohini wishes to fit three rods together in the shape of a right triangle. If the hypotenuse is 2 cm longer than the base and 4 cm longer than the shortest side, find the lengths of the rods.
Paul is x years old and his father’s age is twice the square of Paul’s age. Ten years hence, the father’s age will be four times Paul’s age. Find their present ages.
