Advertisements
Advertisements
Question
The hypotenuse of a grassy land in the shape of a right triangle is 1 m more than twice the shortest side. If the third side is 7m more than the shortest side, find the sides of the grassy land.
Advertisements
Solution
Let hypotenuse=h, and other sides by x and y (x bigger than y). As per the question,
h= 2y + 1, x = y + 7 .... (i)
For right angled triangle, x2 + y2 = h2 ... (ii)
Putitng (i) in (ii), we get:
(y+ 7)2 + y2 = (2y+1)2
⇒ y2 + 49 + 14y + y2 = 4y2 +1 + 4y
⇒ 2y2 -10 y - 48 = 0
⇒ y2 - 5y - 24 = 0
⇒ y2 - 8y + 3y - 24 = 0
⇒ y (y - 8) + 3 (y - 8) = 0
⇒ (y+3) (y-8) = 0
⇒ y = 8
⇒ x=y+ 7= 15, h = 2 x 8+ 1 = 17
Hence the sides are 8, 15, 17 cm.
APPEARS IN
RELATED QUESTIONS
Solve the following quadratic equation for x : 4x2 − 4a2x + (a4 − b4) =0.
Solve for x :
`1/(2x - 3) + 1/(x - 5) = 1 1/9 , X != 3/2, 5`
The speed of a boat in still water is 8 km/hr. It can go 15 km upstream and 22 km downstream in 5 hours. Find the speed of the stream.
Solve the following quadratic equation for x:
`4sqrt3x^3+5x-2sqrt3=0`
If \[\left( a^2 + b^2 \right) x^2 + 2\left( ab + bd \right)x + c^2 + d^2 = 0\] has no real roots, then
If one root of the equation 4x2 − 2x + (λ − 4) = 0 be the reciprocal of the other, then λ =
The sum of the square of 2 consecutive odd positive integers is 290.Find them.
Solve the following equation by factorisation :
x(x + 1) + (x + 2)(x + 3) = 42
Solve the following equation by factorisation :
`sqrt(3x^2 - 2x - 1) = 2x - 2`
Car A travels ‘x’ km for every litre of petrol, while car B travels (x + 5) km for every litre of petrol.
- Write down the number of litres of petrol used by car A and car B in covering a distance of 400 km.
- 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.
