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
Solve the following quadratic equations by factorization:
`(x-1/2)^2=4`
Divide 29 into two parts so that the sum of the squares of the parts is 425.
There are three consecutive integers such that the square of the first increased by the product of the first increased by the product of the others the two gives 154. What are the integers?
The sum of the squares of two numbers as 233 and one of the numbers as 3 less than twice the other number find the numbers.
The difference of squares of two number is 88. If the larger number is 5 less than twice the smaller number, then find the two numbers.
The product of Shikha's age five years ago and her age 8 years later is 30, her age at both times being given in years. Find her present age.
The product of Ramu's age (in years) five years ago and his age (in years) nice years later is 15. Determine Ramu's present age.
Solve the following quadratic equation by factorisation.
2y2 + 27y + 13 = 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.
Solve: x(x + 1) (x + 3) (x + 4) = 180.
